The reasons are "simple". All other axioms and postulates appeal to our "everyday experience", at least in principle. The straight lines correspond to light rays in everyday experience. However it was probably already recognized by Euclid, that the parallel postulate is different from the other axioms. Of course, a degree of mathematical sophistication is required to understand this. But probably Euclid already understood this. Even when stated accurately, the V postulate looks much more complicated than the other axioms and postulates.

How indeed would you verify it experimentally? The postulate itself, or any of its immediate consequences. One of the simplest consequences is that the sum of the angles of a triangle is equal to two right angles. How can you verify that this holds in real life? No measurement, no matter how accurate will show you this.

Gauss and Lobachevski, who recognized that the postulate does not follow from the rest of the axioms, indeed discuss its possible experimental verification. One has to measure the angles of a very large triangle to do this. And any result that you obtain will have some error in the measurement, and leave the possibility that if you take a larger triangle, you will see that the sum is not equal to two right angles.

EDIT. To obtain a better intuitive understanding what the axioms mean, imagine that you live in a world in which one of the axioms is not satisfied, and explore how different this word looks. For example, suppose that two light rays can intersect at two points. This means that under certain conditions you will see the same object as two objects. Our everyday experience shows that this is not the case in our world.

Now imagine a world where the parallel postulate does not hold. Will you see something peculiar in your everyday life? The answer is "no". Everything will look more or less the same. Until you start measuring the angles of large triangles. But we do not really have everyday experience with measuring angles of large triangles.

The reasons are "simple". All other axioms and postulates appeal to our "everyday experience", at least in principle. The straight lines correspond to light rays in everyday experience. However it was probably already recognized by Euclid, that the parallel postulate is different from the other axioms. Of course, a degree of mathematical sophistication is required to understand this. But probably Euclid already understood this. Even when stated accurately, the V postulate looks much more complicated than the other axioms and postulates.

How indeed would you verify it experimentally? The postulate itself says that through every point A not on the line L one can draw only one line parallel to L. How would you propose to check this experimentally? There are clearly many lines through A which intersect L so far away that you cannot see this. So they do not intersect within your field of view.

Or one can try to verify any of its consequences. One of the simplest consequences is that the sum of the angles of a triangle is equal to two right angles. How can you verify that this holds in real life? No measurement, no matter how accurate will show you this.

Gauss and Lobachevski, who recognized that the postulate does not follow from the rest of the axioms, indeed discuss its possible experimental verification. One has to measure the angles of a very large triangle to do this. And any result that you obtain will have some error in the measurement, and leave the possibility that if you take a larger triangle, you will see that the sum is not equal to two right angles.

EDIT. To obtain a better intuitive understanding what the axioms mean, imagine that you live in a world in which one of the axioms is not satisfied, and explore how different this word looks. For example, suppose that two light rays can intersect at two points. This means that under certain conditions you will see the same object as two objects. Our everyday experience shows that this is not the case in our world.

Now imagine a world where the parallel postulate does not hold. Will you see something peculiar in your everyday life? The answer is "no". Everything will look more or less the same. Until you start measuring the angles of large triangles. But we do not really have everyday experience with measuring angles of large triangles.

The reasons are "simple". All other axioms and postulates appeal to our "everyday experience", at least in principle. The straight lines correspond to light rays in everyday experience. However it was probably already recognized by Euclid, that the parallel postulate is different from the other axioms. Of course, a degree of mathematical sophistication is required to understand this. But probably Euclid already understood this. Even when stated accurately, the V postulate looks much more complicated than the other axioms and postulates.

How indeed would you verify it experimentally? The postulate itself, or any of its immediate consequences. One of the simplest consequences is that the sum of the angles of a triangle is equal to two right angles. How can you verify that this holds in real life? No measurement, no matter how accurate will show you this.

Gauss and Lobachevski, who recognized that the postulate does not follow from the rest of the axioms, indeed discuss its possible experimental verification. One has to measure the angles of a very large triangle to do this. And any result that you obtain will have some error in the measurement, and leave the possibility that if you take a larger triangle, you will see that the sum is not equal to two right angles.

The reasons are "simple". All other axioms and postulates appeal to our "everyday experience", at least in principle. The straight lines correspond to light rays in everyday experience. However it was probably already recognized by Euclid, that the parallel postulate is different from the other axioms. Of course, a degree of mathematical sophistication is required to understand this. But probably Euclid already understood this. Even when stated accurately, the V postulate looks much more complicated than the other axioms and postulates.

How indeed would you verify it experimentally? The postulate itself, or any of its immediate consequences. One of the simplest consequences is that the sum of the angles of a triangle is equal to two right angles. How can you verify that this holds in real life? No measurement, no matter how accurate will show you this.

Gauss and Lobachevski, who recognized that the postulate does not follow from the rest of the axioms, indeed discuss its possible experimental verification. One has to measure the angles of a very large triangle to do this. And any result that you obtain will have some error in the measurement, and leave the possibility that if you take a larger triangle, you will see that the sum is not equal to two right angles.

EDIT. To obtain a better intuitive understanding what the axioms mean, imagine that you live in a world in which one of the axioms is not satisfied, and explore how different this word looks. For example, suppose that two light rays can intersect at two points. This means that under certain conditions you will see the same object as two objects. Our everyday experience shows that this is not the case in our world.

Now imagine a world where the parallel postulate does not hold. Will you see something peculiar in your everyday life? The answer is "no". Everything will look more or less the same. Until you start measuring the angles of large triangles. But we do not really have everyday experience with measuring angles of large triangles.