In poultry it is understood that a trio means one male and two females. If you are exhibiting, it is required to be in that ratio.
A male line and a female line are not named simply for the sex of the first bird you choose to make a pairing to start that line. A male line refers to a line in which only the males have the characteristics needed to fit the Standard description. Females in this line usually have traits which disqualify them. It sounds counterproductive, but a line like this may be used to produce exceptional specimens of one sex for exhibition purposes. In some ways it simplifies things, because you do not have to worry about trying to achieve Standard qualities in the sex for which your line is not bred for. A female line would be the opposite, only the hens have the required exhibition characteristics. In some of these seperate lines, breeding a quality male of a male line to a quality female of a female line does not give you offspring that resemble either parent. Usually seperate sex lines are needed at the variety level. It is unfortunate that some varieties will never breed true, according to the standard requirements for both sexes in one line. If you wish to exhibit both sexes of these varieties you must keep both a male line and a female line. This is called double mating. For more information on this, see Bantam Chickens by Fred Jeffrey, published by the ABA.
I don't know where you get the idea that the female sets the type. Both sexes contribute equally, except if you have a prepotent individual, but that is uncommon.