What is one reason European governments protect the growing if food with subsidies even though imported food would be cheaper?

Answer 1

There are a number of reasons, but these three here are the most important:

1) Food Security: The Developed World is paralyzed by the thought that if they rely on importation for their foodstuffs from Africa, Latin America, and Asia (the regions of the World that economically-speaking have a comparative advantage in agriculture), they will suffer through famines and hardships the same way that poor African nations do. They subsidize their agriculture to make it a viable form of security against famines elsewhere in the world.

2) Bioengineering: European organizations are scared of American and Canadian penchants for bio-engineered food products. Europeans are unsure whether or not these hormone-induced animals are safe to consume and wish to promote a tried-and-true method of food production that they believe is safe for their society. (This is why buying American products instead of subsidization is out of the question.)

3) Entrenched Practice: The European States (and now the EU) have been following this policy of supporting the farmers in their countries, that it would be very difficult to remove it. Farmers (especially in France) form a very powerful lobby for the protection of their benefits. Furthermore, considering how much money France pumps into the European economy, many countries are reluctant to try to alienate it by requesting that these programs stop.

Answer 2

It encourages them to grow certain products and also makes up for losses when they they are growing products that are not doing well and helps farmers whose farms don't produce as much revenue as some large scale farmers do. All of this helps things even out and helps agriculture do better across the European Union.