...猫の写真を見ないですむと思うと、同情しろという方が無理だった。
When he thought that he could get away without seeing any cat photos, sympathy was impossible.
In my translation I've condensed all of 同情しろという方 into just one word: sympathy. I'm struggling with how to unpack this. One problem is that I don't know whether 方 is ほう or かた. I can think of two ways this might go:
- 同情しろという方{かた}が無理だった - a person saying that you should be sympathetic would have been unreasonable.
- 同情しろという方{ほう}が無理だった - the side of him that said he should be sympathetic was impossible/unreasonable.
I think option 2. makes more sense but I'm not certain.