First point, I no longer work in the food industry (not for 30 years) but from a business standpoint, I see a couple of things that are telling me that you are not being singled out for the shredder...
"He seems to ***** at me a lot whenever he is there. Then all the kitchen managers say I'm doing a great job. The other cooks say that he is just giving me a hard time. I do take what he says into consideration, it seems like he's really pushing me though. He says I'm too slow and I have to go faster, but then the managers are saying I'm fast and doing really good work... The next day he is all nice to me... "
The owner doesn't hate you. If he did, you'd be gone a long time ago. He has a lot riding on his staff, and it sounds like he sees you as a promisimg prospect for future advancement. That is what I read out of your other comments below. We'll get to those now...
"The owner is there most days and yes it is in a kitchen of a chain restaurant. Once in a while he works the grill. Other times he helps at prep. He's usually out of there early though. I think he does these hardcore checks once in a while. Maybe I just don't understand the management of a restaurant yet... Is this how they keep people on their toes? It's not only me, he complains to everyone about something. I still fear that he'll fire me though... "
A chain restaurant where the owner is a franchisee is a huge investment (and if this is his only franchise, you can bet he probaly has all of his eggs in one basket). That makes for a lot of stress for the owner, and some of that is going to trickle down to (or explode all over) the staff. I bet if you were to talk to the FOH, you'd hear about how they can't do anything right, either...
Maybe there were some financial problems that were making him crazier than normal, I don't know, and you shouldn't ask...
The owner sounds to be "hands on" which means he isn't above getting his hands dirty, too. This is a trait which might simply let you know that he has an inkling of what it takes to get the food out, and is not above pitching in where his efforts might help get the day rolling or the customers served.
Take comfort in the fact that the other folks are getting ragged at, too. That shows that it's not just you. Small consolation, but take what you can get...
"Is there anything I could do to make this situation better? I think I need to speak with the kitchen managers first since they keep saying I'm doing good work... I told the owner this and he said only my opinion counts, it is my business... Last month he told me that I have come a long way and he wants me to take it up another notch."
The last two sentences in the above tell a ton.
First, he sees his restaurant as a business, and not a popularity contest. He may value the opinions of his kitchen managers, but does not base his decisions solely on their input. He's in the kitchen and takes his own notes.
The last part is the kicker.
He's watched you progress, likes what he sees, and thinks you have untapped promise to be better.
You might take the initiative to mention to him that you would be interested to learn what his ideas are to get you to that next level/notch. Specifically, what do *you* need to improve upon, and does he have any suggestions on how to help you succeed.
Point blank, improving your skills/output/technique generates increased production, hopefully satisfied customers, and that means that you *both* have succeeded.
Try to look at this as an opportunity to excell, and at the very least, you'll have some valuable learning experience.
Not that it's crucial for the situation, but you never mentioned how long you've been in the industry, and I get the impression that this may be your first job in a commercial kitchen. If so, the jitters are to be expected.
As a final point, don't paralyze yourself over the prospect of having to unexpectedly find other employment. Work hard, work smart, and absorb all you can about your current position.
Should you be shown the door, you're taking away more than just your paycheck, you've gained knowledge which makes you more valuable to your next prospective employer.
I believe I can honestly say that *ALL* of us have had the occasion to "don't let the door hit us in the @$$..."
Best of luck!