"What sport do you like?"
Translation:¿Qué deporte te gusta?
That is a correct statement, which I guess is the reason it was downvoted.
Learning the qué/cuál patterns may be easier for some people than all this rule lawyering. Those patterns are the approach used at https://www.realfastspanish.com/vocabulary/que-vs-cual
If I remember correctly from Spanish class, there are only two ways to conjugate "gustar"--gusta, and gustan. You use gusta when the object you like is singular, and gustan when the object you like is plural (for example, "I like sports"). You change the "me", "te", "le", or "nos" part depending on who the subject is (as in, you like is "te gusta", I like is "me gusta", he/she likes is "le gusta", we like is "nos gusta"). So, in other words, the phrase "te gustas" doesn't exist.
If I'm wrong, someone please correct me, but otherwise, I hope you get it now!
Well, in general, you are correct but there are cases in which gustas or gusto can be used. Here are some examples. Me gustas - I like you (this generally has romantic overtones). La gente es generosa si les gustas - People are generous if they like you. ¿Crees que le gusto? - Do you believe he/she likes me. And do not forget past tense usages of gustar. Me gustó más la primera forma - I liked it better the first way.
And te gustas can exist. Eres rico, un buen partido y te gustas a ti mismo - You're rich, eligible and you like yourself.
There is no need for a because there is no indirect object noun and no person as a direct object. The literal meaning is closer to:
What sport is pleasing to you
That's why there is no need for a.
A Juan le gusta el deporte?
That sentence needs a because Juan is an indirect object. Does that help?
I realize the sentence is asking about a singular sport, but that is not a question that is often asked in conversational English. We would ask "what sports do you like" I wish Duolingo used more of Corpus Linguistics to generate more natural language. It would be helpful to learn phrases people actually say. I guess i could assume that this is a natural and normal sentence in Spanish, but I highly doubt it.