Internet Interests

This is a poem which has that hint of sarcasm that I love to write/read. I think the sentiment is strong and relatable, what's left is to make the word choices stronger and more memorable.

Why do I love you?
I hate loving you.
Elaborate here. Hate is vague, and could possibly be replaced, but more important would be the addition of a line here that shows how much you hate it. What is comparable to that annoying feeling that you cannot get rid of? Mosquitoes?
But everytime
You ask me another question
What kind of question? Instead of vaguely mentioning a question, use a specific, and give a sample response below, instead of "my mouth won't close". Make it a generic question, like "Can you move down a seat?" and give an awkward response like "Sure, I love your shoes"... or something better...
My mouth won’t close
Because maybe if
I told you just one more thing about me.
Just one more thing.
You’d love me too.

Your poem has a touch of wryness that reminds me of Billy Collins. Collins deals with dialogue in a really great nonchalant manner. Whatever words appear in his poems are always very simple but deal so well with the situation. He never cheats and only mentions the words in passing. The remarks are important. For example:

until the hour is nearly noon
and the snow is piled high all around us;
then, I hear him speak.

After this, he asks,
can we go inside and play cards?

Certainly, I reply, and I will heat some milk
and bring cups of hot chocolate to the table
while you shuffle the deck.
and our boots stand dripping by the door.

In his poem "Shoveling Snow With Buddha" a completely nonsensical situation is made particularly surreal with that one bit of dialogue. Do the same with your poem. Add in dialogue, because it will make the poem distinguish itself, and because it will give your situation depth. Right now, we're reading about a ironic, common situation. Now you need to pitch us straight into the situation with specifics. I think Thornton Wilder made his plays so specific that they ended up being universal.

That's a very cute poem.

Er...one thing's bugging me though...

My mouth won’t close

Sure it shouldn't be "open"?? Cuz if you don't keep your mouth close, it'll be open and you'll say things about yourself, right?

This bit confused me.

No constructive criticism though.

Oh, I don't get the significance of the title.