Hello ottilia112,
We understand being able to send quality videos on your iPhone. Are they appearing the same when you view them in the Photos app on your device? If so, it could be related to the camera itself.
We'd recommend checking your settings on the device first. Here's a great article to help guide you: Record HD or 4K video with your iPhone or iPad
Also, have you tried to see if this happens when you send over cellular or Wi-Fi? That can help to narrow down the issue. We'd make sure that the device is updated to the latest version of software available as shown here: Update your iPhone, iPad, or iPod touch
You may also want to check with the receiver to see if they appear blurry when they are getting the videos. If not, you may check your device storage to see if you have enough space to store the videos in high quality as shown here: How to check the storage on your iPhone, iPad, and iPod touch
Here's another article to help with sending those videos through the Messages app: Send and receive photos, videos, and audio messages on iPhone
These articles should help to clear this up.
Take care!