In the TV show M.A.S.H. why is Frank Burns character portrayed as such a childish person? Everything he does seems childish. (I absolutely can't stand the character and feel for the actor who played the part.) (Childish may not properly encompass my feelings, but I can't think of a better word.)
To answer this, you have to consider the source material which is the film and the book that came before it. In the original material Frank Burns is a very different creature. While as inept as the character in the series, the film/book version is far stronger in his own personal beliefs and (unwarranted) confidence. Film-Burns goes so far as to blame others for the shortcomings of his lack of surgical knowledge and crushes a young orderly, blaming him for the death of a patient.
The book/film shows the danger created in wartime by drafting doctors to surgical duty who didn't necessarily have the ability yet still got promoted in the chain of command. It further shows the lengths that competent doctors went through to get these people thrown out of the army.
In transitioning to the series which wanted to still be drama mixed with comedy; albeit lighter fare so as to be accessible to 70s audiences; Frank Burns in his film/book state needed to undergo some changes.
So, ratchet down the incompetence, ratchet up the child-like goofiness and you've still got "A" Frank Burns.
In the long run, the character didn't last the series and left under similar pretenses. Winchester was brought in spinning the film Frank in the other direction. High level of superiority and confidence, but removing most of the incompetence in exchange for cultural snobbery.
One last note on your comments.
Actors will tell you that villains/unlikable characters are far more fun to play. The fact that you find yourself brought to an emotional level over the character on a regular basis is a sign that the actor was succeeding at his work. Linville himself said he had a love/hate relation with the character. The actor himself was a very sweet, bright, well-liked gentleman, but really relished making Frank as conniving as he did.