"For" case in "The man is fishing for fish"

[leke]

In the sentence, "The man is fishing for fish.", would for fish be and example of the dative? I'm questioning this because I thought the dative benefits the noun it affects, but the fish in this sentence are not benefiting being fished for (if you know what I mean :-D).
For example, I think this is dative, "The man is fishing for the children." ...that is, for their benefit.

Thanks in advance

 

[5jj]

It is not helpful to think of the 'dative' at all in modern English.

The most useful way to consider 'for' in the first sentence is as a preposition meaning 'in order to obtain sth' (Oxford ALD). With this meaning, it collocates frequently with such verbs as look, hunt, fish, etc.
In the second sentence, 'for' is simply a preposition 'used to show who is intended to have or use sth' (Oxford ALD).