Why does my cat only cuddle with me when my dogs are not around? Is he afraid to lose his street cred?

Maybe he just wants your full attention.
If I still had a dog I'm fairly certain my cat would be the boss, even the raccoons are afraid of her. 😼

He probably feels like you're a place where he'd be disturbed by the dogs when they're around. As they come to you and probably disturb him. Hence chooses calm moments

some cats are quite proud

Because she in trouble

Yes

Yup