Why did Jefferson ask for an embargo against Britain and France?
At the time Britain and France were fighting a set of huge worldwide wars known as the Napoleonic Wars and they had both imposed embargos on the other. It was very difficult for the US being very young and with British trade making up almost all of its exports (and yet France being a traditional ally) for the US to remain neutral. However it had to because it had no real standing army.
Anger was developing against the Royal Navy because with the large Navy at its command conditions were very poor in British ships and often sailors would hide as crew on American ships. The British tried to reserve the right to search American ships for stowaways but often mistook Americans for British sailors as there was no discernible difference in accent yet. However Napoleon had expected the Americans to be more supportive of him due to French help during The Revolutionary War. When the US showed it did not want to get too involved French policy, particularly naval, became more aggressive towards the US. So to defend his mercantile fleet from impressment and capture by the French (but also as a sign of defiance at the Europeans pushing the US around) he implemented an embargo. Unfortunately it did much more damage to the US than to the Europeans.