Center on canvas is not exact

I suspect that the image is centred, but the layer has content that matches the background so you can't see it.  Or something like that.

Drag a guide out to the centre of the image — it should snap into place when you get it close.

Select the layer your are trying to centre, and hit Free Transform (Cmd T)

If the centre handle intersects the guide, then it is centred

To center your image precisely in Photoshop, use the following steps: select the image layer, go to Edit > Free Transform (Ctrl + T), and manually adjust the image position by entering exact values in the options bar. Alternatively, use the Align tools in the top menu while holding Shift to ensure it's perfectly centered. If you still experience discrepancies, check for any hidden guides or snap settings that may affect placement.

Can you describe the steps to center? Are you selecting all before centering? Problems can arise if you have a width or height in pixels that is not divisible by 2, such as 1501, otherwise, everything works fine. Remember to select all and choose the layer with content before centering.

2) I want to center and image that is 5" width on my 8" x 11" page-canvas

4) I have a MM ruler.

By @kathleen27066899kazr

Photoshop works in pixels, not inches or millimeters. For testing purposes, can you change your units to pixels and tell us if that works when your center your image?

I branched your post from a primary thread about aligning multiple layers to each other.

https://helpx.adobe.com/photoshop/using/aligning-layers.html

Jane