Are the hydrogen atoms of 2-methylindane homotopic, enantiotopic, diastereotopic or unrelated? I'm very confused. According to the answer key, the circled hydrogens of 2-methylindane (2-methyl-2,3-dihydro-1⁠H-indene) are diastereotopic. I thought they were enantiotopic.

My thought process is the following. They aren't homotopic because replacing one of them with another atom would create a chiral center. Due to them creating a chiral center, I thought it was enantiotopic.

I thought that for it to be diastereoptopic, the carbon with the methyl group off of it would have to be chiral as well, but I don't think it is chiral. The molecule is symmetrical off both sides. Does diastereotopic rely on that carbon being chiral after the new atom replaced the hydrogen? If so, then I understand.

I was under the assumption that the state of that carbon must be chiral before the hydrogen is even replaced.
The process to determine whether two protons are enantiotopic or diastereotopic is to replace each with deuterium and look at the relationship of the resulting compounds. For the indicated hydrogens in 2-methylindane, replacement of each gives a pair of diastereomeric compounds (Figure, top). The compound also contains enantiotopic protons (Figure, center). The carbon where the replacement happens doesn't necessarily become a stereocenter in this process (Figure, bottom).