So, I want to make an animated profile picture for myself, but, I don't want to use other applications or 3 party software to convert it because of privacy reasons. Also, I don't have a windows computer, only mac. Please help me!
Drop to GIF (available at GitHUB) and GIF Brewery (Apple Store) both accomplish this task natively and locally on Mac OS without uploading anything anywhere. Drop to GIF is super lightweight and small footprint, but has few bells and whistles. GIF Brewery has a lot more features, but cost a small amount of money (I don't remember how much, but cheap) when I purchased.
If you use Screenflow (advanced screen capture and markup tool Mac OS specific) then know that this supports pretty advanced GIF export on its own.
And lastly, depending upon which version of the Mac OS you're running, on the latest, High Sierra, you may not need any of these at all: Photos (newer replacement for older iPhoto) will export GIFs natively - from iPhone Live Photos or videos according to the documentation.
I like to use EZGIF Video to GIF tool (they have many other awesome GIF tools)
It's very simple and easy to use it, that's why I prefer using it.
Just Drag-n-Drop you video into the "Choose File" box, and hit Upload Video
Then choose your options and convert - wallah, it's all good.
The problem may be not wanting to use "3rd party" stuff due to privacy... Most "free web video to gif" things will require you to upload the video.
You might try the suggestions from this article at macworld.co.uk
The article details how to use the iPhone, and also provides some Mac-based applications for creating animated GIFs.
Use an online converter like Convertio.