Any ideas why my father doesn't seem to be able to eat anything?

There is a whole protocol to assist people who have swallowing disorders (dysphagia) and he should be assessed, usually that is done by a speech and language pathologist but sometimes a registered dietitian.
But you don't need to wait for a formal diagnosis to start thickening his drinks and modifying his foods to a degree that makes eating safe.

https://www.agingcare.com/articles/swallowing-disorders-tips-for-using-food-and-beverage-thickeners-208048.htm

https://www.agingcare.com/articles/dysphagia-how-to-help-a-loved-one-eat-and-drink-safely-187010.htm

He can receive PT for swallowing after he is tested and the need medically necessary.

Your dad has a lot going on. From your profile he has
At 65 years of age:
Cancer, Anxiety, Arthritis, Depression, Hearing loss, Heart Disease, Lung Disease, Mobility problems, Parkinson's Disease, Sleep disorder, Stroke, UTI and Vision problems.
Is dad on Hospice?
If he is eating it may be time that all his foods are pureed.
His fluids may need to be thickened as well. There are times when the body can not distinguish between fluid, food or air so sometimes the passage to the lungs does not close when eating or drinking and food or fluid ends up in the lungs. This can cause Aspiration Pneumonia.

Has your father had a swallow study?

Call his doctor and request one. Immediately.

Liquids can be dangerous to someone with impaired swallowing. He may need thickener added to them.

Aspiration pneumonia can kill.