What you call minifying is actually removal of indenting. Minifying would mean the complete removal of all spaces, tabs and line breaks from your code, outputting it into one line, eventually compressing all your CSS
in one file and all JavaScript
in another.
Tidy is not capable of preserving the original indenting of the markup from the input it receives. That’s because Tidy starts by building a clean parse tree from the input, and that parse tree doesn’t contain any information about the original indenting. Tidy then pretty-prints the parse tree using the current config settings. Trying to preserve the original indenting from the input would interact badly with the repair operations needed to build a clean parse tree, and would considerably complicate the code.
Complete documentation here.
If you want to keep your indenting, stop using Tidy.
Response to proposed change by Amanda: I do not agree "if you want A, don't do B" is a hostile phrase construction and "If you want A, consider not doing B" should be used instead. For me, the second construct has more hostility, since it is a common structure for ironic comments. I don't want that. When I advise my very own kid, with the best intentions, not to put his hand on the stove if he doesn't want to get burns, I don't say "consider not putting your hand on the stove". I say: "If you don't want to get burns, don't put your hand on the stove." [Informative. Friendly. Not hostile.]