Macbook Air logs out when I touch the mouse pad

Hello ,

Thank you for reaching out to Apple Support Communities.

Your Mac shouldn't logout as soon as you touch the mouse pad or trackpad.

Let's check to see if you have Hot Corners enabled:

"Use hot corners on Mac

You can use the corners of the screen as hot corners, to quickly start actions when you move the pointer to a corner. For example, you can start the screen saver when you move the pointer to the top-left corner of the screen, or lock the screen when you move the pointer to the top-right corner.

Tip: By default, the bottom-right hot corner is set to Quick Note, so you can quickly open a note to jot down your thoughts at any time. See Start a Quick Note.

1. On your Mac, choose Apple menu  > System Settings, then click Desktop & Dock  in the sidebar. (You may need to scroll down.)
2. Click Hot Corners on the right.
3. For each corner you want to use, click the pop-up menu, then choose an option, such as Notification Center, Launchpad, or Lock Screen.
4. To use a modifier key with the hot corner, press and hold the Command, Shift, Option, or Control key, or a combination of these keys, while viewing the pop-up menus.
5. Click Done."

More details can be found here: Use hot corners on Mac

If the issue persists, can you provide a few more details? Which macOS version do you currently have? When did you first notice this? Also, does this happen when your Mac is asleep or while in use?

Cheers!