I downloaded 3-4 vector images that for some reason do not give me an option to use the layers in Photoshop. Why is this happening?
Sorry to hear that.
If you are opening vector files in Photoshop then please follow the steps as mentioned below in order to see the layers associated with the files:
Go to Files>Export>Export as Photoshop(.PSD)> choose the color model>and select the option "Write Layers"
If you still face troubles, please let me know the File IDs with which are facing troubles with so that we can further assist you.
Also, depending on how the image was set up and saved in Illustrator (or whatever app was used) the artist selling it can do a lot to make it more or less useful to the end user - sometimes everything is on one (Illustrator) layer, sometimes grouped randomly or nonsensically, and sometimes all the paths have been converted to a single compound path before the file was saved and uploaded.
This makes it as hard as possible for the end user to modify the vector (which is part of the license), and it also makes it so there would just not be any layers to use in Photoshop - just the main / background layer.