I understand the idiom ‘go off the deep end’ could mean ‘be irrationally carried away’. However, ‘go off’ sounds like ‘leave’ but the idiom suggests a meaning of ‘heading for the deep end’, which alludes to the deep end of a swimming pool, according to some ‘grapevine’ source.
The idiom alone does not carry the sense of ‘heading for’, Haihao. To add that sense to ‘go off the deep end’, you would have to say something such as “He’s going to go off the deep end”.
I agree with your grapevine source that ‘the deep end’ refers to the part of a swimming pool where ther water is the deepest. However, to me the words ‘go off’ in the idiom have more the meaning of ‘jump into’. (Definitely not ‘leave’!)
The expression is also ‘go off at the deep end’. There are other meanings of ‘go off’. It can mean ‘go bad’ when used to describe food that has turned rotten. It can mean ‘start to dislike’ in the sense of:‘I used to like Charlie but I have gone off him recently’. It can, as you say, mean ‘walk away’. It is also used with the idea of ‘explode’ when referring to bombs. Perhaps the last one is nearest to the idea in your expression. ‘At the deep end’ is often used to describe the most difficult situation. When someone starts a new job and is ‘thrown in at th deep end’, they have to deal with the worst problems. This ‘deep end’ could indicate an excessive or extreme situation. Putting all this together we come to the meaning of the expression: ‘go off the deep end’, which I would suggest means ‘lose your temper’. Breaking it down into parts you then have, as I see it, a picture of someone exploding (figuratively) to an excessive extent.
Well, now that you’ve also got answers to additional, unasked questions, Haihao, I’d just like to make sure you (and Alan) understand that my comment about ‘go off’ being similar to ‘jump into’ addressed your question about the literal meaning of the idiom and its literal reference to a swimming pool. The literal meaning of the words in the idiom might be described as ‘(suddenly) enter the pool where the water is deepest’.
I understand “at the deep end” the same way Alan described it. I have heard it used with a few differerent verbs, but always combined with 'in’ (and never with ‘go’ or ‘off’).