Oh, that's right, he says it can't lead to eternal life, even though Jesus tells us it does.
JESUS did not say that following the Law would yield (for us) eternal life.
Rather, JESUS, when approached by those wishing to know the way to eternal life, answered with the only answer that was available at the time ... obey the Law. Didn't mean that one could actually successfully travel this path, ... only that it was the only way.
This was not a declaration that any attempt to follow the Law could actually result in eternal life, only that following the Law was the only way which currently existed.
All of this was, of course, prior to JESUS' sacrificial death on the cross, for, once this was accomplished, there was another way to gain eternal life ... through JESUS and the power of His sacrifice.
To be fair, JESUS spoke of this way (i.e. I am the Way, the Truth, and the Life ... Noone comes to the Father but by Me) also to those whom He chose.
Paul simply taught from the perspective of the sacrificial death of JESUS having already occurred.
And now a question for you ... If we can gain eternal life by keeping the Law, ... why did JESUS have to die ?