Here is another way to explain why there is no induced emf and therefore no induced current in the loop, (which is equivalent to the earlier explanation). Consider the following loop moving at velocity V through a uniform magnetic field into the page. At the top and bottom of the loop, where the conductor is orientated parallel to the direction of V, there is zero induced emf. At the front and back of the loop, where the conductor is orientated normal to the direction of V, the induced emf is a maximum. However, the direction of the induced emf from the front and the back always exactly cancels out, provided the magnetic field strength is perfectly uniform, so there is no net emf in the loop. For every segment around the loop that you can consider, you can argue from symmetry considerations, that every segment of the loop that experiences an induced emf is exactly cancelled out by the diametrically opposite segment. Hence there is zero net emf in the loop. I hope this makes sense.
View attachment 38793