Is it bad to be stubborn?

It's not a hard and fast thing as it would depend on what you are being stubborn about.

You call me stubborn; I say I'm determined.

You call me pig-headed; I say I've considered the issues carefully, and I'm sure I'm right.

You call me a fanatic; I say God has spoken to me and told me what to do.

Some people are unable to ever admit they've made a mistake. That's often a sign of deep insecurity, delusion, or sheer ignorance. (The current occupant of the White House is a good example of this sort of behavior.)

On the other hand, rational, intelligent people are sometimes called stubborn by those who don't have the skills or evidence to persuade them to change their minds.

If your boyfriend calls you stubborn when he's trying to get you to do something you just don't want to do, that suggests he's lashing out in frustration. Maybe he just needs to accept you have the right to make decisions about what happens in your life. If he thinks your decisions are wrong, he should go away and think of ways he might persuade you to change your mind.

If your boyfriend calls you stubborn because you're one of those people who always sticks to their guns, even when it's clearly to their disadvantage to do so, then maybe you should consider why you need to do this. You might be missing out on good things by being so inflexible.