Why the option isn't there
Compression in Adobe's world lives in two features — Reduced Size PDF and Optimized PDF — and both belong to Adobe Acrobat, the paid application. Adobe Acrobat Reader is the free viewer. It opens, prints, annotates and signs PDFs, but it does not rewrite them, and file size reduction means rewriting the file.
If you go looking in Reader's menus you may find a compress entry that leads to Adobe's web service or to an upgrade prompt. That is not Reader compressing your file; it is Reader handing the job somewhere else.
Your three options
1. Adobe's online compressor
Free for occasional use, no software to install, and it handles files up to 2 GB. You choose High, Medium or Low compression. Your file is uploaded to Adobe's servers, processed there, and deleted unless you sign in to save it.
This is the path of least resistance if the document is not sensitive and you only need it once in a while. Use it often and you will be asked to sign in.
2. Buy Acrobat
If you compress PDFs regularly, or you need to hit an exact size with control over what gets sacrificed, the full application is the proper tool. The Acrobat method is written up here, with the exact menu paths for Windows and Mac. Worth it for a job that involves documents daily; hard to justify for a one-off form upload.
3. Compress it in your browser
A browser-based compressor avoids both the subscription and the upload. Our PDF compressor runs entirely on this site in your own browser — you pick a target size such as 1 MB or 500 KB, and it compresses to fit. Nothing is sent to a server, so there is no copy of your document anywhere to worry about.
The honest trade-off: it works by turning each page into an image, so text in the result is no longer selectable or searchable. For a scanned document or a form you are uploading, that costs you nothing. For a contract someone needs to search, it does.
What Reader is still good for
None of this makes Reader useless — it is the best free PDF viewer there is, and it does a lot that people pay for elsewhere. You can fill in and sign forms, add comments and highlights, read documents aloud, and view protected files. It simply does not rewrite the document, and compression is a rewrite.
A note on quality
Whichever route you take, compression is lossy for images. Compress a file once and the result is usually fine. Compress the already-compressed version again, and then again, and the damage accumulates visibly. Always keep your original and compress from it each time rather than compressing the compressed copy.