Mueller testified under oath. Statements of fact fall under the rules of perjury.

He has just testified that he met with POTUS and discussed the position of Attorney General. He said as a matter of fact that he did so not as a candidate for that position. This claim introduced a dispute of fact.

He has also testified that he does not remember if, during that same meeting, he discussed the firing of Comey. The fact at issue here is not whether or not he did discussed the firing, but that he claims to not remember whether or not he did so.

That this would have disqualified him at the outset is of enormous significance to his acceptance of the job offer from RR, as this would constitute a clear conflict of interest directly bearing on the investigation itself.

These statements of fact (plus the underlying need to fact-find about what was discussed in the meeting with POTUS) open Mueller up to questioning beyond his written reports (vol 1 and vol 2). He is before the Judiciary Committee of the House and his credibility is on the front burner now. As Grassley forewarned just before this moment in Mueller's testimony.

As a strategic and procedural matter, this has given the Republicans an edge. How they pursue it on the House committee – or on the Senate committee – is up to them. Think of it as gaining the advantage in a set during a tennis match.

When POTUS considered firing Mueller, he was also fully co-operating with the investigation. Firing Mueller would not have ended the investigation. If there was reasonable grounds to remove Mueller, there could be no legal issue. However the greater concern was the political cost of firing him.

The decision to fire or not to fire was one of politics. It would look bad such that political enemies would use it to promote moving toward impeachment. And that is a political matter. Counter-balancing such political optics would be difficult, given the complexity of revealing what POTUS and Mueller had discussed the day before Mueller's acceptance of his appointment as Special.

That said, complaint against Mueller, from Mueller's own report, is that Mueller had serious conflicts. Firing a member of the team investigating does not mean eliminating the investigation, obviously. Consider that Mueller had just testified that he had done this very thing when he fired Strzok. The position was filled by someone else and the team continued on its way. Remember, there remains a dispute of fact about the firing of Strzok – was it for actual conflict of interest (i.e. bias) or for the appearance of such (as per Strzok's testimony)? Regardless, by either measure Mueller acted on firing a key player on his team, a senior member, a leader, without obstructing the investigation. This is very like what POTUS wanted to do but, based on the political balance, decided not to push to conclusion. He did not fire Mueller but he maintained him - conflicts and all. Mueller fired Strzok - actual or apparent conflicts and all.