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When you're married or in a serious relationship, your life becomes part of the other person's life. Decisions should not be made solo, but be shared as a couple. This guy isn't doing that. He's making his choice, to leave for a career, regardless of what his girlfriend decides she wants to do. At least that's how it seems from the letter. And comparing a daughter to a career? Eeesh. The LW is absolutely right - a child is a part of you, like a limb - not something interchangeable like a career.
What kind of a parent would this man make, if he has the same feeling towards his children, or his partner's children, as he does towards his career? Something interchangeable, to be exchanged for a better model, if necessary?
To the LW: this guy isn't willing to stick his neck out for you, or his child. Unless he himself demonstrates, through actions, not just through words, that he wants to stay with you, make a committment to you and your daughter - then there's only pain to be had from chasing after him. Sadly, Cary is probably right: if he wants to leave, it's time to let him go.