I agree with Student 1. The cause of the seasons is indeed the tilt of the Earth's axis. As the Earth orbits around the Sun, the northern hemisphere is tilted towards the Sun during the summer, and away from the Sun during the winter. This causes the northern hemisphere to receive more direct sunlight during the summer months, leading to warmer temperatures and longer days. At the same time, the southern hemisphere is tilted away from the Sun during the northern hemisphere's summer, causing it to receive less direct sunlight and leading to cooler temperatures and shorter days.
While it is true that the difference in distance between the northern and southern halves of the Earth is relatively small compared to the distance between the Earth and the Sun, it is the angle of the Sun's rays that is more important in determining the amount of sunlight and heat received by a particular region on Earth. This is because the angle of the Sun's rays affects the amount of atmosphere the sunlight has to pass through, and this can cause the sunlight to be more or less intense, depending on the angle.
In conclusion, the tilt of the Earth's axis is indeed the cause of the seasons, and Student 1 is correct in their understanding of this phenomenon.