Did I miss something?

Memory serves that an attacker used to be in an offside position, in part, if he was in his opponents’ half of the field. Now, it seems, that attacker is given a yard +/- because he is not offside if he is in his own half of the field. So, ignoring the opponents, if an attacker has a foot on the half-way line, marking both halves, is he not in an offside position?

USSF answer (February 22, 2012):
An area of the field is demarcated by lines. The lines belong to the area they define. The halfway line belongs to BOTH halves. Foot position (or body position, for that matter) at the kick-off is treated similarly to the foot position for a throw-in: The foot may be on or behind or hanging over the line. For offside, the only thing that matters is where the parts that can legally play the ball are. However, in all cases, the offense, if any, is TRIFLING. Therefore, a player with his foot on the halfway line can be said to be in his own half of the field of play, no matter that some parts of his body may be across the line in the opponents’ territory.

For pure territorial purposes, yes, a player whose farthermost advance is a foot on the midfield line is indeed still in his own half of the field; however, the “formula” for determining if an attacker is “past” the second-last defender (past = any part of the body that can legally play the ball is closer to the goal line than the second to last defender) would apply as well to determining if an attacker was past the ball or past the midfield line. In other words, if any part of the body that can legally play the ball is across the midfield line, then the attacker is indeed in the opposing team’s half of the field — for purposes of determining offside position.