that's a weird exceptional case with sevmek/beğenmek. If I see your new shirt, I would say "Gömleğin ne güzel, çok beğendim!" and never ever "çok beğenirim/beğeniyorum"; while in English one would use the present tense.
Similarly, one would say " bu ayakkabıları beğendin mi?" when he asks for the opinion about the shoes.
(of course we accept the present tense in Turkish too, as it depends on the context. For example here if you your friend has been using the shoes for a while and you want to ask him how he likes them in general, you would say "bu ayakkabıları seviyor musun?")
Building on what Selcen said, there is a similar phenomenon with the verb "to miss" özlemek. I am not sure why, but it is just normally used in the past. (You are probably on the right track witht he emotion having already happened thing that you said). These are the finer points of Turkish grammar that many people never master and you caught it! :)
Why, thank you. I have to say that I have really fallen in love with Turkish. I did Barış's Hacking Turkish courses and lots of vocab on memrise, and that got me a good enough passive knowledge to read Harry Potter (what else? :-)), but doing your course has made such a big difference for my active language usage. The other day I had my first conversation in a doctor's waiting room with a Turkish lady. I think she was as excited about it as I was. I had such a big, happy grin on my face.
Just one more question: How would I express that I missed or liked something/someone in the past then? Do you phrase it like 'dün seni özledim'?
If you talk about liking soup in general as in "I like soup", beğenmek doesn't really fit you should use sevmek or hoşuna gitmek: Çorba(yı) severim/Çorbayı seviyorum/Çorba hoşuma gider.
beğenmek is preferable in specific situations but you should again use past tense; you take a sip and then say "çorbayı beğendim" - and never ever "çorbayı beğeniyorum"
"çorbayı beğeniyorum" only makes sense if you talk about a specific soup in a general sense, e.g. "Annemin yaptığı domatesli çorbayı beğeniyorum": I like the tomato soup that my mom makes.
Well, but ayakkabı is made up of "ayak" + "kap" in the possessed form.
It seems that "ayakkabı" has merged together so strongly that it's considered to be a basic word and endings go on the end (e.g. plural "ayakkabılar", definite accusative "ayakkabıyı"), whereas some other words, though also written together, still obey the noun-noun construction, e.g. "havalimanı", airport, from hava + liman, which has definite accusative "havalimanını" and plural "havalimanları". Though "havalimanılar" is also found, but much much less often according to Google.
The situation seems to be confused, though - I see both "havalimanıya" and "havalimanına" as well.
Thanks for this discussion! Turkish often uses 'past tense' to express liking something (or a preference for something) in the 'present'. Eg. "Hediyeni sevdinmi"? ("Did you like your gift"?) ... (even if you are asking this presently, right after they unwrapped the given gift).