Even if you are a very successful writer, criticism can hurt.
Try really hard to consider the source. Could this person be jealous or envious of you because it is something they always wanted to do? If you think that is the case, then encourage them to start writing. Is this person someone who is always negative? If so, then just let it slide off your shoulders. It isn't worth acknowledging. Every writer needs encouragement, well honestly, every person needs encouragement. But when you are a writer, you seek that encouragement out, you listen when others give you feedback. It's what we do.
So, how do you handle it if you are receiving unwarranted criticism from a friend and/or family member who may or may not have even read your work? Family is always going to be one of two types: 1) they will LOVE everything you write and not give you true feedback... or...2) they will criticize everything you do, because, well, that's what they do!
You should seek criticism out because you need to hear it. You need it to allow you to grow. No one's work is perfect, and someone may have a fantastic idea that you hadn't thought about. But, seek constructive criticism and the best place to find that is with your peers. Seek out other writers.
If someone is criticizing your writing and hasn't read your work, how can they know if you are a good writer or not? Hand them some of your writing and suggest that if they are going to criticize, they should read your writing so they have better ammunition! Maybe once they do read your work, they can offer some honest criticism. If they refuse to read it, then kindly ask them to not just your work if they have not read it. Perhaps it is actually you they are criticizing and not your work....so just look at that person as they truly are.
What if someone has read your work and offers criticism? Take it for what it is. Not everyone's style is the same. As a writer, you want criticism, because it makes you a better writer. Listen to what they have to say, review your work based on their suggestions and see if it makes sense. If their suggestion is just a conflict in styles, then go with your gut. You know how to write, so don't be dissuaded by negative feedback. Take it with a grain of salt. If they offer some really constructive feedback, then make the changes if you think it will make your work better.
Stop taking it personally. I know, it is personal because it is your work. It is hard to hear, but the more feedback you get, the easier it is to take. So, just hang in there and realize your own self-worth as a writer. Put on your Big Girl Panties...and WRITE!