The direct forces at the clew, head, and tack of the chute are pulling forward, forward/leeward, forward/up/leeward (respectively) from the boat, thus not pushing the bows down. However, the force on the rig as a whole is acting 15, 20, maybe 25ft up the mast. This induces quite a moment in the system which is reacted by a couple that pushes the bows down and pulls the sterns up. The boat is in "pitching equilibrium" (for lack of a better description) when the force of the chute pulling up on the tack equals the force pushing the bows down. This is also helped along by the skipper and crew moving aft in the boat. The force of the skip and crew weight counteracts the upward force of the sterns.

Ultimately there must be a net down force for the system, otherwise the FAA might get involved.