This is not that easy to schedule as full balance is impossible. If you had 10 persons, there there are 25 possible mixed sex partnerships, but with 2 partnerships in every match you can never have all partnerships exactly once, so the next possibility is 12 persons, for example:
[(M1 F4):(M5 F6)]
[(M6 F2):(M3 F3)]
[(M4 F5):(M2 F4)]
[(M5 F1):(M6 F3)]
[(M2 F2):(M6 F6)]
[(M3 F5):(M1 F1)]
[(M4 F6):(M5 F3)]
[(M6 F4):(M1 F5)]
[(M2 F1):(M5 F2)]
[(M6 F1):(M4 F4)]
[(M2 F5):(M1 F3)]
[(M3 F2):(M5 F4)]
[(M4 F1):(M1 F6)]
[(M3 F4):(M2 F3)]
[(M5 F5):(M4 F2)]
[(M2 F6):(M3 F1)]
[(M4 F3):(M1 F2)]
[(M6 F5):(M3 F6)]
But note that it is not possible to have everyone play against each other the same number of times, above the three pairs (M1 F2), (M3 M4) & (M5 F5) never oppose each other. To have a truly balanced schedule, each player has to have one other player with whom they never partner or oppose (see the spouse avoiding
schedules here.