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.
But inviting someone to like your page isn't an invitation to critique. It's not asking a question. Uninvited criticism on a non CC page is like accepting an invitation to a wedding and asking for all to hear why the groom married such an unattractive and stupid woman when he could have done so much better by getting someone younger and thinner and richer...
Unsolicited invitations to "like me or like my page" are nothing more than spam, digital junk mail. Let's face a little reality about Facebook and other sites like it. It cost you nothing, not one red cent. To those that use it, it is nothing more than some FREE advertising. Oh Goody Goody..................... You get what you pay for and you expectations should match that cost as well.
Facebook and other "social media" sites like Facebook gives you this "service" so you can be their carnival hawker to draw them in a crowd. They make their money from all the unsolicited ads they have. Same spam, same digital junk mail. I don't want to pretend I'm a farmer, I don't want to pretend I'm a mofioso, I don't want to crush some candy and I don't want unsolicited "please suck up to me" invitations from the Facebook tools. If you stick fliers on every door in town inviting every unknown Tom, Dick and Mary to your wedding well you are going to get those that have questions and opinions. If you don't think it will happen then you need to get back to the real world or perhaps be a bit more selective in your invitations.
You have a brick and mortor store and someone paints all over the store front, you have a legitimate beef. You buy a domain name, pay someone to build it for you and pay your monthy fee and somebody hacks it again a legitimate beef. Remember if you build that site you don't have to build into it the ability for others to respond or leave comments.
Perhaps taking a trick from the big companies would be a better way to go. Instead of complaining about lemons and throwing them in the trash, make lemonade. Many of the most successful sites don't delete the unfavorible posts, they address them often supplying additional advise, rectifying the problem or even admitting that what was suggested might have some merit and will be looked into in the future.
Like I stated all along, I am not defending the OP or thier actions, both parties lacked tact in the situation. The fact is this is "Social Media" which means a little give and take. S#!% happens sometimes and people get a little askew, but to get your panties all in a wad because you didn't get the the comment you wanted while using some freebee you are taking advantage of equally as tacky.