That often depends on the structure of the subsidy.
"We will pay you 5 euros per kg of fish sold in supermarkets to consumers" is different from "We will pay you 500,000 euros a year to keep fishing".
There is a very reasonable argument in fisheries starting at least a century ago (and locally long before that), that we're looking at a partially renewable good - that it would be easy to cause an unsustainable population collapse with unrestricted harvesting, and so you should try and intervene in the market to sustain fish populations and stabilize harvests. Subsidies intended to do this are distinct from subsidies intended to keep fishermen employed fishing.
"We will pay you 5 euros per kg of fish sold in supermarkets to consumers" is different from "We will pay you 500,000 euros a year to keep fishing".
There is a very reasonable argument in fisheries starting at least a century ago (and locally long before that), that we're looking at a partially renewable good - that it would be easy to cause an unsustainable population collapse with unrestricted harvesting, and so you should try and intervene in the market to sustain fish populations and stabilize harvests. Subsidies intended to do this are distinct from subsidies intended to keep fishermen employed fishing.