так и

- Ты умеешь плавать ?
- Немного. А ты?
- Я учился плыть, но так и не научился. Боюсь воды.

Everything is clear except for "так и", however one can guess it. Can you help? Tks

I think that the correct meaning is:
- You can swim?
- A little. And you ?
- I tried, but couldn't learn not even "a little" . By fear of water.

так и in negative sentences means 'still' or 'finally' .
'Я учился плыть, но так и не научился' is something like 'I tried, but still cannot' or 'I tried, but I hadn't managed finally'.
By the way, 'учился плыть' is a little bit wrong. 'Учился плавать' is more correct.

- Can you swim?
- A little. And you?
- I tried, but I still can't swim (or "but I haven't learned it yet"). I'm afraid of water.

"так и" implies that there have been many attempts to learn to swim and the person has been trying hard, but so far to no avail. Each time the person ended up in failure.

the phrase is так и не.

It translates as never.

Я учился учился но так и не научился плавать.
I took swimming courses out the wazoo but never learned to swim. or: but never did learn to swim.