Why do some countries protect their own market from other countries products?

They try to maintain the independency of their own economy. If they allowed import with low or no taxes, the imported products might be cheaper than the domestic products. That would result people buying the imported produce. That would make the domestic produce more expensive, because there would be overproducing. The domestic providers would then have to downsize their production, thus creating unemployment.

The more unemployed people, the less money they have to spend = vicious cycle.

Preventing similar items that are largely produced domestically can protect the entire country spiraling into bankruptcy.