Generally speaking, people are permitted to delete their own answer, and Stack Exchange tries to respect that preference when possible.
This is a good thing. It seems like common courtesy towards the answer. Also, it is good for the site and our mission overall. Assuring people that they can delete their answer may help people feel more comfortable posting answers, knowing that they can delete it. For instance, I know that I have had situations where I wrote a detailed answer that seemed valid to me at the time, and probably looked good to others, but then I subsequently realized was flawed, and I deleted it to avoid spreading confusion. If the site didn't allow me to do that, I might be more reluctant to post answers in the future. Thus, perhaps counter-intuitively, knowing that there is always the possibility to "undo" an action (e.g., posting an answer) can help people feel more comfortable doing the action in the first place.
There are some specific cases when it's not possible to delete an answer. If an answer is accepted, then the site does not allow the author to delete it.
Also, there are exceptional cases. If someone makes a pattern of repeatedly abusing the ability to delete answers, then you can flag for moderator attention, to ask moderators to look into it. For instance, if a user was posting many answers and routinely deleting each of them after 3 days, that would be a bit dodgy and not in line with the mission of this site, so if you were to spot such a pattern, I would recommend flagging for moderator attention so they can look into it more closely. You personally might not be able to detect this, but people with 10,000 reputation or higher could. I wouldn't bother them with isolated cases, but I do realize there could be exceptional cases where this becomes a pattern that is harmful to the community. That said, I think you'll find that exceptional cases and abuse are extremely rare, and generally not worth worrying about.
I know it's not much comfort when there was a specific answer you wish you could see again, but maybe it is some comfort to know that the ability to delete answers contributes to people feeling comfortable to answer, and thus contributes to this site being such a great resource that often gets you fantastic answers.
Rather than trying to dig up that deleted answer (which, who knows whether it is even valuable), I think your time might be better off seeking answers to your question in general. Perhaps there are edits that can improve the question (e.g., work on it more on your own, following the hints given to you, and show what progress you've made in the question), or perhaps once you have enough reputation you can offer a bounty to attract attention to it.