The manual and may sites tell, the dwarfs with high constitution are immune to poison. He has a score of 19!
It can`t be better.

Why can every spider poison him??

Being resistant is not the same as being immune.

Ok, but I got poisoned with every bite.

Unlucky. Every action is done with the roll of dice; Your Taghor keeps rolling poorly.
Whenever you can, dodge enemies. Move forward, strike, move backwards/sideways. It's very important to not tank enemies but to move around. This becomes more and more important as you travel deeper.

Is he wearing armor?

Being poisoned is not that bad. When someone gets poisoned, I let my cleric cast slow poison and we deal with the poison after we left the spider area. You come across a few cure poison potions, then.