You seem to know the correct meaning of the word, but the phrase doesn't make much sense to people who are not skilled at deciphering things. For example, we will not write "to" in front of a verb for no reason, although they apparently.do that in Français.
The meaning of "debate" is when two people (or perhaps two groips or a group of people who each has their own opinions independently) argue academically about a topic, usually either scientific or political, and MEANT to be non-aggressive.
You can debate anither human being, a verb, or you can go to a debate, an intangible noun. You can also "have a debate".
"to debate", in the way you are saying it here, is never said, although you might say "I want to debate Richard Seaman about the effectiveness of the war in Malaysia", which is unrelated to your use of "to".
What you'vr written here also doesn't make sense in another way. First, you've written, specifically, that you could not find a certian example. Then, you specifically wrote that you DID find examples, the exact opposite of what you just said a sentence ago.
Secondly, this is the only possible use of the word "debate", so it is impossible for any website or database that includes the word "debate" to not have such a definition, unless it is used in some other way such as to discuss the frequency of occurance of the letter T in English or something.