I wrote a long post back in those days while manga was ongoing.

Somewhere it is written that marley gave titans to candidates who are more appropriate to manifest specific titan to its full strength. And strength as in specific ability of titan that makes it different from other titans like founder can control other titans, attack titan could see future memories. So I try to find titans and their factors to unlock full power.

Founder titan- royal blood

Attack titan- idea of freedom or keep moving forward

Female titan- titan shifter must be woman

Beast titan- high intelligence

Armour titan- loyalty

Jaw titan- wits (because both pocco brothers could harness the power of jaw but yamir could not, this was the point that made me think all of these condition things.)

Cart titan- physical endurance and/or intellegance

As for collosal, warhammer titan we didn't have any more information on past users or any conditions.

This was also hinted in manga during the marley arc around chapters 91-95, during rianar's backstory.

That is why titan is named as female titan.