I have no doubt that you'd like to be the case, but it is an illogical argument. There is only one legitimate basis for opposition to legalized abortion, and that is the belief that it is the moral equivalent to murder. An example of this belief is the Catholic Church's teaching that life begins at conception, and therefore an unborn person has the same right to life as any other person. An athiest can (and often does) come to the same conclusion, but the uniformity of the religious teaching makes it easier to point to. Obviously, there is no conclusive evidence to prove or disprove this belief. Meanwhile, as the legitimate argument for a pro-life position is the respect for human life, it stands to reason that someone who was pro life would also oppose euthanasia for the same resons.
Nope.
All one has to support is the belief in individual freedom and self-determination.
That would mean that anyone from a baby to an adult has the right to choose for himself whether to live or to die.