Welcome to Android Central! The bottom line is that you can't send it using standard MMS, due to the severe filesize limit that MMS has always had (about 1 MB). Yes, you can send big videos over iMessage on iPhones because that's Apple's proprietary messaging system that they're not going to share with anyone else. You can simulate it on Android phones by using another messaging platform that can handle videos well, like Telegram, but that means the other person has to be on that same platform. Hopefully, RCS will fix this, but the big US carriers have been doing their best to stymie this because they want to promote their own terrible messaging platforms.
In the meantime, do what was suggested above and upload the video to your Google Photos or YouTube and share the link privately.