Wrong. SCOTUS got involved because there was a group of feminists and abortion activists who had been trying for years to overturn state abortion laws, but knew they wouldn't be able to have success in any but a few states, CA, and NY being the largest ones. They discussed this with lawyers and came up with the idea that they needed some legislation that could be shepherded to the Supremes to get one big fat ruling. This had been discussed with Justices at the Supreme Court who were also interested in making abortion legal.
They decided to do it in Texas, which was the largest of the states that still had anti-abortion laws, and Sarah Weddington introduced a client, who Weddington claimed, wanted an abortion, but couldn't get one because of those laws. She sued for her client's 'right to privacy', and the case made it all the way through the appeals process, guided by pro-abortion activists all the way, to the Supreme Court, where Justice Brennan and his pro-abortion co-horts were sitting on ready to make null all state abortion laws by their ruling.
Turns out, the client, Norma McCorvey was pregnant, but NEVER WANTED AN ABORTION. She just went along for the ride. She later became a Christian, repented her involvement in Roe-V-Wade, and is now a prominent pro-life speaker.
Thanks, I was unaware of the detail.