While I get the concept, remember the OP was INVITED to like the person with the facebook page. I was taught long ago by my mother...... If you don't want to hear the answer then don't ask the question. Samething could apply here. If you don't want responses from people don't go asking them to "Like" you or your facebook page.
In this particular case BOTH lacked a degree of tact.
Invites to like a page are not open invitations to critique photos. I'm not sure if you have a facebook page or not or if you are familiar with how facebook works, but there are many different types of pages, personal ones, business, artist, community entertainment etc., plus group pages. Most group pages are closed and you must join them. On group pages, critique is often asked for and given openly, but group pages and personal pages are much different than artist and business pages. I have invited people to like my artist page on facebook, but I would not tolerate anyone giving open critique of my photos, because that's not why I post them there. My page is a gallery of my work. As I said somewhere else in this thread, on facebook, if someone doesn't like a photo, then ignore it, or you send a PM to the artist or business owner. Its called good manners.