Lots of dogs (actually most) don't really like being picked up. And actually, that's quite fair enough - even aside from the precariousness of being carried in someone's arms, just the act of wrapping your arms around a dog is a very dominant/threatening gesture
in dog terms. We don't think of it that way, of course - but we're primates, and wrapping your arms around someone is more about warm fuzzy stuff than threats and domination. Thing is though, for your puppy to start feeling comfortable with it,
he needs to recognise that you don't mean it in the terms another dog would.
I would not be worried about the growling and biting. Consider the above, then you've got to acknowledge that it's actually a fair reaction. He's not comfortable and probably feels threatened (normal dog reaction, remember). So he lets you know to back off please. You probably (well, certainly) are ignoring the subtle/polite signals and persisting. So he growls. You still persist, so he snaps at you. He's not being aggressive, he's being defensive.
Your choices thus are two. One is to simply stop trying to pick him up. The second is to back off a bit and work to gain his confidence till he can understand that, from a human, arms wrapped around him or being lifted isn't the threatening gesture he thinks it is. I'd recommend the latter course. Not because you're likely to spend massive amounts of time when he's bigger trying to lift him. But because the majority of humans never consider that gestures that have warm fuzzy connotations in primate terms (like hugging) have the opposite connotation to dogs. So it's perfectly likely that some strangers, kids included, are going to rush up and try to hug your dog at various times throughout his life. Now, you're never going to make the dog love being hugged
But you can work to desensitise him to it, gain confidence, and realise that it's not a threat from a human. There's much less risk of him being surprised and reacting defensively then when confronted by some strange human trying to hug him. Do take it slowly though, and back off a bit if he's defending. It's confidence he needs, not to be forced.
