It's the most direct route to freedom
While climbing up the oesophagus would make more sense, there are a few things to consider that make bursting through the chest a better option.
Chestbursters grow incredibly quickly, and can vary in shape and size. They could very well not fit in a human throat, and then have to claw their way out if they get stuck, making the whole exercise a waste of time:
Growth of the Chestburster is rapid; the creature's signature inner jaw is known to form within an hour of implantation
They soften up the chest cavity before bursting through (what a gross sentence), so it's not an especially hard task:
When fully developed, the Chestburster releases enzymes that soften the bone and surrounding tissues of the host's chest cavity to facilitate its egress, before finally forcing its way through the sternum.
But of course, there's always the non-canon Facebursters from Alien 2: On Earth