This is a little technical, but I think Raab did actually have a valid argument here. Let's look first at what he said with relation to section 13 in the Marr interview which I assume you're referring to.
AM: Well, let’s come back to what may or may not happen. You say that,
you know, you were worried about aspects of the deal. You voted for
the withdrawal agreement, and for a lot people who are proper
Brexiteers, that was betrayal. You said you wouldn’t vote for it and
then you did.
DR: It’s not quite true is it, Andrew? If you look and
read my speech, what I said was I voted, in the specific third vote we
had, was to avoid the European elections and any further extension,
and it was very clear that if we were going to have a vote on the deal
under so-called section 13 – I can bore you with all the detail – it
would have to come back to the House of Commons. So I voted only to
avoid an extension, which I think was a bad idea. And I think I’ve
been proved right about that.
AM: Let me read you what you said on the Today programme in November.
‘If you just presented me with this deal or EU membership. yes, I
would think this is even worse than that,’ staying in the EU. ‘We’d
effectively be bound by the same rules without a voice or control over
them.’ That’s what you said. Worse than staying in. But then you voted
DR: So let’s be clear and honest with your viewers about this
in relation to the backstop, which is the suite of laws we’d be bound
by. We wouldn’t have any say over those and we wouldn’t be able to
exit them. No democratic country in history has agreed to be bound by
that. And I voted against an extension, but I made very clear, as my
speech in the House of Commons shows, that because we would have
another section 13 vote that I would reserve my position.
The section 13 Raab is referring to is of the European Union (Withdrawal) Act 2018 and can be viewed here. The important bit here is paragraph (1):
(1) The withdrawal agreement may be ratified only if—
So for the withdrawal agreement to be ratified by the Government, the withdrawal agreement and the framework for the future relationship need to be approved by the House of Commons.
Let's now look at why the third 'meaningful vote', which Raab is being asked about in the interview, did not constitute such a motion. The vote took place after the first two meaningful votes failed, and you may remember that then-Speaker John Bercow stopped the motion coming back a third time due to parliamentary procedure stating that "a motion or amendment “which is the same, in substance” as something already voted on should not be brought forward again in a session of parliament."
In order to get around this, the Government removed the approval of the Political Declaration from the third motion, the text of which can be found here. It refers to the decision of the European Council published on March 22nd which stated that if the Withdrawal Agreement alone was passed by Parliament, an extension would be given to the Brexit process until the European elections on May 22nd. If the agreement was not passed, a smaller extension until April 12th. At this point, the UK would have to "indicate a way forward" in order to obtain a further extension.
Note that the motion itself acknowledges that it doesn't "meet the requirements of section 13(1)(b) of the European Union (Withdrawal) Act 2018".
Now that we have all of that information, it is fairly clear why Dominic Raab supported the motion. He sets out three reasons in his contribution in the House:
First, it is necessary to satisfy the EU Council decision on 22 March
to avoid and indeed prevent the Government returning to the EU to seek
an even longer extension. I regard that as essential.
This refers to the fact that if the Withdrawal Agreement were not passed, the Government would be free to agree an extension which could potentially be fairly long with the EU. On this point, Raab was proven correct - the UK negotiated an extension to October 31st.
The second implication of the motion, by virtue of that, is to avoid
the UK holding European elections in May. I regard that as absolutely
essential to avoid the very dangerous and corrosive effect on public
trust in our democracy.
This refers to the fact that if the Act was passed, an extension to May 22nd would be automatically given. Clearly a precondition of staying in the EU via a Brexit extension is to hold EU elections. At this date, it would be too late to hold such elections, and the UK would therefore presumably leave the EU.
The third implication of the motion is that under section 13 of the
European Union (Withdrawal) Act 2018, a duly constituted third
meaningful vote will have to return to the House for a vote,
presumably on Second Reading of the withdrawal and implementation
At last, we come to the crux of Raab's argument. Under section 13, the motion in question is insufficient to allow the Government to ratify the deal. Therefore, the Government will have to return to the Commons with a new motion which does. Raab is pointing out that voting for the motion doesn't bind the UK's hands, and allows for further negotiations with the EU.
In conclusion, Raab didn't see that voting for the motion had any disadvantage, in that it wouldn't allow the Government to ratify the Withdrawal Agreement, which he had fundamental disagreements with - and a clear advantage in that it would give the Government what he saw as an upper hand in negotiations. It would have triggered an extension of the negotiation period to May 22nd, the expiry of which without EU elections would have presumably mandated the UK's immediate withdrawal from the Union. As the motion would not have allowed the Withdrawal Agreement to be ratified, this would have either have occurred on a 'no-deal' basis, or under a Withdrawal Agreement and Political Declaration which would have had to be approved by the House of Commons in a further vote.
I've tried to be as clear as I can here - let me know if there's anything which doesn't make sense!