Hmm, I never really thought about it, or if I did I shrugged it off. Hmm, I can't come up with an answer. as Hulavuta said it doesn't really help you anymore to insert yourself into your character whether you had a father or not. Infact, in recent games they even began giving your mother a backstory and sometimes a name. In DPP your mother is named Johanna who was a Pokemon Contest star (and friends with Fantina), in BW your mother said she was a trainer (and on her journey is when she encountered your father, another trainer at that time), in BW2 your mother was a Pokemon Center receptionist and been all around Unova, and in XY your mother is named Grace who's a famous Rhyhorn Racer (and its her being a Rhyhorn Racer that convinced Sycamore to give you the Pokedex
to get you away so he can bang your mom). So if the intention was to provide a blankest slate as possible they sort of failed being two of your moms are famous.
So why only a mother yet not a father? Well it is sort of implied that being a trainer is sort of a job so your father could be on his own journey. The Pokemon World seems to be some kind of utopia society where it's not really a questionable thing for a parent to be away from his family for a long period of time on a journey battling with magical monsters. Norman's Gym isn't in Littleroot but rather two cities away in Petalburg, Palmer is off on a secluded island being the Tower Tycoon and probably hasn't come home in years judging by the way
Barry and him act upon seeing each other (and if I remember correctly Palmer and your father were friends and your friendship with Barry is compared to their friendship), Janine is left to run the Fuschia Gym while her father Koga is off being a member of the Elite Four (and not to mention all the other kid Gym Leaders). It seems like your father just so happens to be a trainer who's off on a journey and your rival's father either retired or never got into being a trainer. Heck, what parent would let their child run around an entire country and or explore the world on their own and wielding magical monsters that have the capability of causing mass destruction?
But why is the mother there? Well between the two parents a child would have a "stronger" connection with their mother being they're the ones who gave birth to them. Now I know for some people that's not true, family situations are complicated, but in the Pokemon world, at least for the character you're playing, they have mother at home who had taken care of them. The mother is there for pretty much moral support and say it's okay for you to go out and explore the world. It's nice to see them being given more backstory, but for the most part they're just there to give you permission to go on a journey so that you in real life aren't thinking "shouldn't I have some kind of parental guide with me?". Why, no, because your mother said it was okay to go on your own!
Also of your XY rivals we only don't know anything about Tierno. Your opposite gender rival lives in Vaniville Town (has father & mother), Trevor is from Lumiose City (father, mother, older sister), and Shauna's father can be found in Snowbelle City (or at least is implied to be her father, no mother though).
Speaking of missing family members, do any of the player characters have canon siblings? I can't think of a single one. (In fact, why has Game Freak never thought of making the opposite-gender protagonist the player's sibling? It ties up potential alternate universes very nicely.)
Nope, can't think of a single one. Them being your sibling is one way to use them in the game (would they be your twin though?), though I'd always saw them being used as your cousin if they were to be made related to you (since your both suppose to be the same age).
