No 1. Itchy skin
This could be due to itchy skin or objects in the eye. Check if your dog has itchy, swollen or reddened skin.
No 2. To get treats
Your dog might continue to do that for your reactions if you have you rewarded with treats.
No 3. Instinct
In dog language, direct staring is a sign of dominance.
Some dogs might cover their face to avoid eye contact, which signals submissiveness.
When To Worry About It
No 1. Fear or Anxiety
Check if your dog feels threatened in some way. If it is excessive, go see a vet or a trainer.
No 2. Health issues
If your dog not only rubs the face but licks or chews certain areas, this could be caused by allergy. Also, scratching eyes or ears is one of the symptoms of infections.
Lastly, periodontitis could be a reason. When it’s severe, your dog will need teeth extraction. Go see a vet if you see tartar before it gets worse.
No 3. Trauma
Has your dog been bitten by a snake or stung by a bee? In this case, your dog could rub his face because of it. It may not be of a concern, but if it is compulsive enough, consult with a trainer.