Translation:Even though they like tea, they don't drink tea.
literally, פי is a variation of פה (mouth) or edge/opening edge of the abyss = פי התהום
על פי = on the edge = according
אף is short for אפילו = even
It doesn't have to make sense. It's language
Thanks a lot! that was helpful. I know it doesn't have to make sense but i was just curious
I guess it means 'even it was said' or 'even it was in mouth'. See similar על פנה
Would "although" work as well? I didn't try it since it wasn't given as a translation but was the first word I thought of reading the sentence.
They don't quite mean "exactly the same thing" (although they obviously share a lot in common: "though"!). "Even" is an additive, for example, that can be used to add or affirm something that would otherwise be unexpected, or sometimes even(!) "least" expected, relatively speaking. It's often used to add something and intensify it (sometimes at the level of words and list-items, or even(!) at higher levels like clauses, sentences, etc.).
For example, "I like broccoli, cucumbers, spinach, and even asparagus." Alternatively, "I like broccoli, cucumbers, and spinach. I even like asparagus."
Here are a couple examples related to the above translation, which shows that the addition of "even" slightly changes how we construe (or conceptualize) these sentences (even though the basic conceptual content is still the same):
"Though I like tea, I don't drink tea." "Even though I like tea, I don't drink tea."
"Though I dislike fish, I eat fish." "Even though I dislike fish, I eat fish."
Stephen Levinsohn, a linguist and translator, details some of the cross-linguistic uses of such connectives, for example, in "Self-Instruction Materials on [Narrative and Non-Narrative] Discourse Analysis": http://www-01.sil.org/~levinsohns/discourse.htm