that's a shame to hear. but ultimately you'd have to admit your situation is quite rare, relatively speaking - no pun intended
Not sure it's all that rare. I've had relatives pass away, and not felt much in the way of external emotion. Just didn't think of myself as much of a crier, despite loving them very much. However a couple of years ago, our Lab/Collie cross, Bella, had to be put down - and I was in bits for a while. I quite literally broke down in tears over it. And I'm not ashamed about that in the slightest - I loved her to bits.
She was put down on a Monday. I phoned my boss, told him, and said I was going to take a couple of days off. He was understanding, said that (regrettably) it would come out of my holiday, and I was fine with that. Again, I feel absolutely no shame in mourning the loss of a pet.