From my experience I've gathered the best way to make a pet like people is to have them grow up around people. This also goes the same for pets with family.
I've heard of people having problems saying "my dog wont let our babies grandparents near our baby..." Often though, that grandparent doesn't like dogs, so while they're around the dog, they never befriend it so it's always skeptical of them. The grandparents in this case have done it to themselves.
So the moral of the story, is even if you don't like something, that doesn't mean you should ignore it. As in this case, the dog distrusted the grandparents because the grandparents didn't like dogs and thus shunned it.
If you don't want a pet to be overprotective against someone, then make sure the pet is familiarized with the person (or other pet, for that matter).
Disclaimer: As always, use your discretion. For example, if your pet is vicious, it may be too late for the familiarization process. If your pet is a King Cobra snake, you might not ever want to try making someone familiar with it.