iti, Your image shows a solid line not dashed so as you say it's the grid rather than guides. In my experience the grid is solid lines and guides dashed.

In the view menu there's Show Guides and Show Grid so try turning those on and see what you are snapping to.

To add to OMG's good post, in the view menu as well as Snap to Guides there's Snap to Grid, Snap to Canvass Edges and Snap to Path. So I suggest you make sure just the one(s) you want are on.

I find it easy to put Snap to Grid on by mistake when aiming for Snap to Guides as they are next to each other in the menu. Maybe you've done the reverse?

If none of the above then maybe that grid line isn't on a pixel boundary? How far zoomed in is your picture? It does look like the grid line is mid pixel and your attempted crops are to the pixel boundary either side of the grid line. You can't crop half a pixel.

Should work just by dragging the side of the selection and align with the guide in question. Better still, click View>Snap to guides and it will auto align as you drag your selection close to the guide.

It is going to be an uphill journey for you to learn Gimp. Forget how "All other graphics programs" work

As noted earlier, your screenshot shows a grid-line. You can set up on a global basis Edit -> Preferences -> Default Image -> Default Grid Also there in Edit -> Preferences -> Image Windows -> Snapping is a snapping distance, default is quite small 8 pix. It can catch you out. Adjust to suit.

Working on an image, if for any reason you find that the grid is not convenient, colours, spacing etc it can be changed per image Image -> Guides -> Grid (1) . Same place you can set up a guide, blue line that extends outside the canvas. (2).
Grid / Guide lines are virtual, have no physical size. These settings are saved in a Gimp .xcf image.
Grid / Guides / Snapping is toggled On / Off in the View menu.

Thanks yes i understand the guides and manual entry, the grid size i need to look at and see what its set at, i rarely use snap to anything. Good to know about the 8 pixels snap. The images i am working on and resizing already have their size? i mean pixels, so im not creating images with paint etc. I have to deal with resizing the best i can, and never thought about the line cutting through the center of a pixel instead of on its edges. Yes uphill battle, frankly gimp is not my cup of tea, so to speak, I am thankful its available, and of course free.
If you are unsure that the crop is exactly as you need it, use the Crop Tool Options and manually enter Position / Size as required.