So, only one side is supposed to write the bills? I thought there were two parties who have constituents that matter. too.
the president signs them into law - or vetoes them - he cannot write a bill (but sometimes he has a congressman introduce one for him) - but the intent was for him to only accept or reject - not write a bill
there is also something in the constitution that says any bill that raises revenue for the government must originate in the house - not the senate (that is ignored too when senators have their bills introduced by a house member)