This will be my only post about this issue. It's all more complex than this. But this is a basic summary.
To simplify: the Constitution grants certain rights explicitly. It also mentions that there are rights that exist but are not written down in it. However, there is no way to determine what these rights are in the Constitution. It is possible to determine rights from other rights (that is to say that those rights are implicit, can be inferred), and the right to privacy (which isn't explicitly stated) is one of those inferred rights. The right to an abortion is often said to be in the "shadow" or "penumbra" of the right to privacy, which itself is in the "shadow" of other rights. The source for the "right to privacy" is the
Due Process Clause of the 14th Amendment according to advocates.
This was the issue for Roe v Wade, and it's why many abortion advocates have said that it was on shaky ground, which is why people often pushed congress to do something (which they never did) for the last 50 years in order to protect the right to an abortion. The right to privacy is not explicitly mentioned in the Constitution, and because it's not explicitly mentioned then it can be done away with for a number of reasons (in this case because it isn't mentioned). Since there is no mechanism to determine unstated rights (and the idea of these "shadows rights" is somewhat controversial), the decision was to allow people in their states to determine whether to allow abortion or not rather than judges become "activists" and push for their own favored causes to become rights.
If anyone wants to compare this to gun rights, the difference is that it's currently accepted that the right for people to own guns is what the 2nd Amendment says. So guns are explicitly stated, and abortions are a "shadow" of a shadow right.
Some judges (notably Clarence Thomas) have an issue with substantive due process (read the link I put above), and some SCOTUS cases are reliant on it (gay marriage, anti-sodomy, and some other one he mentioned). This is why he called for those cases to be reviewed. It should be noted that he's really the only justice that advocates this position. It should be noted that no one else signed onto his concurrence where he advocated for looking over those cases, so no one else is calling for it (openly, I guess).