Why are we looking for life on Mars??

I've always had this question, why are we looking for life on Mars?? Those interested in Space and how we first appeared will know two ideas of how life first formed on Earth: either some sort of life/cell "material" fell from space or life somehow bubbled up from deep sea. Many scientists say that the latter is much more likely.
We have established that Mars had water on it at some point, this is clear from the deltas and surface texture of the planet that shows there were rivers, lakes etc. However, on Mars, there were never deep oceans, the only bodies of water were relatively "shallow", comparing to oceans on Earth. If life on Earth formed in deep oceans, then surely life could not have formed on Mars because there just wasn't any deep bodies of water for this to happen in. One could argue that life could've formed differently on a different planet. In that case, the "Recipe for Life" (the list with 3 ingredients like heat) should not exist as it is solely based on what life needs on Earth.
To summarise what I'm saying, life wouldn't formed on Mars because there would be no deep oceans for this to happen in (provided that the idea of life material bubbling up from the seabed is correct, or at least taken into consideration) so there is not point in searching on life on that planet. Or am I missing something here?? I would like to read someone else's opinion on this.