Note: I am answering you, but I, personally, did not downvote your answer.
Voting is anonymous
First things first: voting is anonymous. The only people who could tell you definitively why you were downvoted are the specific individuals who downvoted you, who, a year and a half after you posted your answer, may not even be here anymore, or if they are they still may never see this Meta-question.
Second, the net score of your answer is -2, but the vote count is 2 up, 4 down. Assuming whoever voted to delete is also one of the downvoters (a good bet, but I can't verify because I don't know where to look for delete votes), that means 4 people didn't like the answer. I'd say it will be hard for us to even speculate about the motivations of four anonymous people over the course of the year+ since you posted your answer.
Issues with your answer
Having said that, I'll hazard some speculation anyway:
First, despite your declaration to the contrary, the question itself is not acceptable; it was downvoted and closed. A very common pattern on SE is for people to downvote answers to bad questions even if the answer itself is ok, because giving the OP answers encourages him and others to ask more bad questions.
But if that were the only force in play, then @WS2's answer would be downvoted as well, instead of sitting at +3. Right? Right, so...
Second, your answer is very short; it offers neither details nor corroboration. It is pure unsubstantiated opinion. If you want to do that, post a comment. Posting unsubstantiated opinion as an answer proper is bad juju.
Third, it doesn't really address the question as posed. The OP asks about the acceptability of "thanks in anticipation"; you ignored that concern and answered about another phrase, "thanks in advance".
Bottom line: it's a throw-away answer to a throw-away question. SE doesn't want either of those things, and the voting here reflects that.
A general rule of thumb on SE is: expect your answer's final score to be roughly proportional to the effort you put into it. ¹,²
In your situation, my personal inclination would be to accept that I posted a throw-away answer to a throw-away question, and walk away. I might even decide to delete the poorly-received answer myself. But in any case I wouldn't stay up at night thinking about it. I'd focus on building my reputation³ by finding new questions to answer, and putting thought and effort into answering them deeply and well.
But if you really want to rescue this particular answer⁴, then here's what I suggest:
- First, answer the question as asked:
- Address the usage of the original phrase (... anticipation): how common is it, how likely is it to be well-received, in what contexts is it appropriate or inappropriate, etc.
- Second, if you still want to bring it up, particularly if the first part of your answer establishes that "... anticipation" is unacceptable, then offer "... advance" as an alternative.
- Again, detail how common that phrase is, why it is preferable to the "anticipation"-construction, in what contexts it works and doesn't work, etc.
- After offering all that detail, make sure you substantiate all of it. Back up anything you claim with reference to external authorities. Make sure to name those authorities, and where possible, provide live links to the material you're citing.
Sounds like a lot of work, right? Right. That's the point.
¹ As further evidence: though you can't see them, two other users posted substantially the same answer as you, and additionally added a bunch of garbage characters to satisfy the minimum length criterion (because their answer were so short & unsubstantiated), and those answers were not only downvoted to oblivion, but deleted to boot. That's what happens to poor answers in SE; don't take it personally.
² This doesn't always work, particularly for questions which hit the hot network questions queue, but it's a good baseline to start from anyway.
³ That is, the thoughts in other community-members' heads about me, not the number displayed next to my name.
⁴ Maybe because you want to minimize the number negatively-scoring answers in your history, which is legitimate enough.