The problem is, there is no "the corresponding texture of an object". A mesh object can contain faces assigned to many different materials, each of which can reference many different texture images. However, if you've been working on simpler objects than you currently are, that would be easy to miss.
Within the UV editor, Blender generally displays the most image referenced by the most recently selected image texture node. It tries to predict which image you want to see based on the selection state of shader nodes, materials, and objects. (There may be corner cases, which might be considered bugs, but almost meaningless bugs.)
If Blender is not displaying the image you want to see in the UV editor, you can change the image being displayed by entering the name of a different image in the field in the top center of the UV editor-- in your image, the field that reads "Rikka_Face_V3.png". If you'd like, you can see a list of images referenced by your .blend by clicking on the dropdown immediately to the left of that field, and select an image from that list.