to look out for = to look after someone's best interests and/or their well-being
Calvin is being sarcastic because his dad is trying to make him eat something he doesn't like.
"looking out for someone" is an expression that mean you want the very best for that person or are concerned about someone.
One way parents "look out" for their child is by encouraging them to try new things, under the watchful eye of the parent. Sometimes these new things are not enjoyable, but the experience will help build the child's character (help them grow up to be well-rounded individuals).
In the last frame, the boy is being sarcastic. He is eating the food but complaining about how his father "looks out" for him.
(A similar expression today is to say you "have someone's back")
Another interesting point about idiomatic use of language is also exemplified in the last frame. 'That's my...' can be used as a simple demonstrative adjective: 'That's my coat, I recognize the lining'; or even 'That's my dad, the bald one in the back row'. But Calvin is using it in the metaphorical sense 'That behaviour is typical of my...'.
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