"Love is love"? People like to use phrases for the sound byte but I feel they don't understand the concepts they describe.
A pet is great, but they are far simpler creatures, they can't actually understand your emotions or thought processes, they don't have the complexity of people because they are not humans. We all love our pets, but are they even capable of loving us back? Are they even conscious enough to have that kind of though? Again, I'm not trying to shit on OP, I'm glad that this is the saddest he's ever been, because that means he's blessed and I'm happy he has had that kind of experience, and not having your pet around sucks.
However, going from that, to equating the type of endearment pets provide us to actual, human love is insulting to real people.