Disclaimer: I don't own Doctor Who.
The Doctor has loved a great many people, in a great many ways.
Like family, like friends, like one true loves and like passing fancies. Brothers and sisters, a wife, children - oh, yes. He's seen many kinds of love.
The Doctor has seen love that transcends dimensions and barriers and will always find a way (Rose), love that never even left the ground (Martha), love that snapped him out of it when he felt like shit (Donna), love that blurred into and out of his life in a matter of days (Astrid). The Doctor has seen other people's love. Martha and her husband, Tom Milligan, who are almost disturbingly domestic and normal at times.. Jack and his team, who are a mystery to him in that he can never quite tell who's sleeping with who, there's so much sexual tension. Donna and her family, who love each other despite appearances.
And he's learned that nothing lasts forever, and precious little survives long enough to really appreciate.
And he's learned that promises of eternity are far easier said than done.
And he's learned that the best kind of love is the one always there, always present, always constant.
The love of a mother for her child is rather frighteningly similar to the love the TARDIS has for her Doctor.
Because the TARDIS is a constant, really the only one he has.
Because Doctors and companions will come and go, but this, this is forever.
Sometimes, the Doctor thinks that it's only possible to love one thing at a time, because if you could love all you wanted, then you just might burst from all that niceness flooding your veins. And the Doctor knows he loved Rose, and Martha, and Donna, and Sarah Jane, and Jack, and a hundred billion other people, so he wonders why he's not burst yet, but he counts his blessings and continues on.
And he sees worlds, antediluvian worlds and worlds like something in dime paperback science fiction novels, and he loves them all, so he thinks it probably isn't true that you can love only one thing at a time, because wouldn't it just be lovely, to give yourself all to one person, devote your entire self to them, and doesn't existence itself hate anything lovely and sacrosanct and pure?
And the Doctor thinks that, if this is the way of the world, then maybe he doesn't want to be in the world anymore, because it hurts too much. And he thinks that people hurt, with all of their whining and crying and screaming and loving. So sometimes he wants to forget the lot of them, and just pinwheel through space and never ever stop.
But the TARDIS won't let him.
And that, the Doctor likes to think, is true love.