I have a rescue Shih-Tzu. He won't eat out of his food dish unless I am standing there beside him. Even when I put his food on a plate. He doesn't really like dry dog food, so I have been feeding him the chicken and rice stuff. He still won't eat alone. He had to have someone beside him petting him and telling him its OK.
What do I do about this. I have a job and can't be here all day to feed him by hand or to dump his food on the floor.

What does the title "Why won" mean?

If he's an only dog - and there aren't other dogs in the household - I would put his plate down at a certain time every night, take it back up at a certain time every night.

On the other hand - why do you have to feed him "all day"? I had a badly abused dog that stuck to me like glue for months and months. If he wanted to sit next to me while I ate and he ate, what did it matter?

I don't understand your concern.

I've gotten a dog STARTED on his dinner by hand feeding but then that's it. If you are feeding him a good quality, good grade kibble, I'd stick with that.

I'm not a fan of free-feeding in general, meaning leaving food out all day.
My dogs are fed at set times in the morning and at night, they have gotten into so much of a routine if I'm even 10 minutes late feeding them they sure let me know about it!

With free feeding there can be a few problems, the main one being that the dog will pick at the food, having a piece every so often and then not be hungry enough to eat a full meal.

If you feed set meals you may need to still sit by the dog at first, but you can grudually move further away with each meal as the dog grows more accustomed to the routine.

Even though a rescued dog needs more coddling for a while, maybe even a very long while, you don't let him control all aspects of how you treat him. You TRAIN him.
He needs dry kibble in his diet, for one thing, so start mixing it in and gradually increase it until it's the majority of his food. A dog won't starve himself.
As for standing there, I'd pat him for about 30 seconds and say good dog over and over, and then move away. Let him go back to his bowl on his own. Take it away when you feel you want to, and be consistent about it.
My pets get all the kibble they want, with a small amount of soft food on top at dinner time. I subscribe to the theory that they are less frantic about wolfing food down this way, and even my retriever didn't overeat. Others say it doesn't work well for them.

Everyone handles feeding in a different manner. My dogs eat dinner at night. The puppy also eats breakfast (or a meal in the AM), but my older dog has no interest in eating other than at night.

I have clean water and kibble available at all times.

I've never had a dog that overate, I've always had mutliple dogs, feeding has never been an issue.

Like shaz, I'm not a fan of free feeding.. On top of the picking all day long, if you have a medical problem, there is no way for you to know how much that dog is eating. In multiple dog homes, there is a good chance for one dog to eat all the food and you not knowing so until something alarming is happening.

I think Judy already mentioned it... set up a time that is good for you to feed your dog in the morning and at night. Put it down.. hang out a bit in the kitchen or wherever you are feeding the dog. If he doesn't seem interested after about 15 minutes, pick the food up.

Healthy dogs will not starve themselves. He may be extremely scared and nervous. Scared and nervous dogs will not eat. Let him relax and settle down but keep your routine in place. Even though he isn't eating, you will be getting yourself use to this routine. When he does start eating, don't make a big deal. If you are overly exuberant, you may fighten him from the feeding area and it'll start all over again. Working with timid, fightened dogs is a bit more challanging than a confident dog.

What you can also do to help with his eating problem.. heat the kibbles up. Heating releases the oils in the kibble and makes it smell better. This way gets picky eaters to eat. I would avoid supplementing canned food or any table scraps. You want your dog to eat on his own, not eat the treats and nothing else.

Play around with different name brand foods. He may not like the food you are feeding. Unfortunately that may mean you are purchasing and feeding a lower grade quality food. But for right now, that's OK. Get him use to you, your home and your routine. Once he is settled, than transition him to a better food.

If you have exhausted all of these tricks, then a trip to the vet is needed for an appetite stimulant and exam. Sick dogs don't eat, and they need to be seen immediately. After 4 days of eating no kibble, treats or table scraps, to the vet you go.

Dogs are pack animals. It sounds to me like he is treating you, as they do , like the leader of the pack. He is worried about eating without your approval. In packs the leader eats first, and the others don't eat until they are allowed to.
This could be what he is trying to do. He is ensuring that you approve, and that's why he needs constant approval in order to eat. As he settles in, and gains in confidence in his role, this should improve. :)