Why should Iran be closer to any side to begin with? We have excellent relations with China, we have good relations with India and we have had good relations with Pakistan, except some ups and downs. The thing is, Pakistanis can't take it that Iran can also have good relations with India, we should only declare war on India so that some people are pleased.
We won't take any sides, and the same way we don't ask Pakistan to cut relations with Saudis (and we have been hit a lot by Saudi-Pak realtions and the virus that Saudis injected into Pakistan), we won't listen to Pakistan on how we should have relations with India, and vice versa, India can't dictate us how we should treat Pakistan. You are the one who always says interests matter first, right?
We can have excellent relations with all three countries at the same time and except some minor obstacles, we don't have substantial problems with either of countries.
The funny thing is, Pakistan's Arab allies have bigger and better realtions and trade with India, but why blame them? They are Arab 'brothers' after all, they are holy, only Iran is the devil here.