Why can't I drill deep enough into my wall for wall anchors?
You may be trying to drill into a concrete or brick wall. you can remove some outlet covers (e.g., electric, cable) on that same wall to be able to get a peek inside and confirm.  It's also possible that you are drilling into a stud or even a fire break. Both of the above situations are a good thing if you are trying to hang/mount heavy items.

If it is a concrete wall, look into the correct concrete wall anchor for the weight or bolt size you need. You may also need to get a drill bit for concrete if you don't have one.

If it is a wood stud, you may not need to use a drywall anchor.