After 4 months of being in an exclusive relationship, you should have met at least one or more of his friends.
Talk to him about this, so that you know where he stands mentally and emotionally.
Don’t be confrontational about it.
Any perception that you are confronting him results in deceitfulness on his part.
Rather, initiate the topic through flattery, informing him that you have no doubt his friends must be amazing, given how amazing he is as your boyfriend.
Having had a close relationship with this dog, it is harder for him to grapple with the loss, causing him to be exceedingly upset that his beloved dog has died.
Unsure of how to approach this, you contemplate how you need to behave or what to say.
Avoid overthinking or overstepping your boundaries.
He is the one grappling with the grief.
Let him be the one to dictate how much support he needs from you.
Listening to these instincts is of benefit to you, as they give you a perspective on how you have been behaving thus far in the relationship. 
Talk to him about this, so that you know 
Although you are clueless about why, he isn’t clueless about his reasoning. 
Once you are courting each other, knowing each other’s intent early, benefits either party.
Unsure of how to approach this, you contemplate how you need to behave or what to say.