If I understand Barr's argument correctly, there was no obstruction of justice because:
1) There was no underlying crime.
2) There was no intent (the POTUS is as innocent and naive as a newborn);
3) The obstruction didn't succeed.
All of this is false; and I mean false as a matter of legal analysis. It may be on the way to a determination of whether or not prosecution is worthwhile; but that's not how Barr presented it. Barr presented it as exoneration, as "proof" nothing happened, nothing to see here, move along. He didn't present it as an analysis of the law (and it's the kind of analysis that would mean you'd failed Criminal Law in law school), he presented it as a set of facts, without allowing anyone to know what the facts actually are.
This is a brazenness John Mitchell would never have dreamed of expressing.
"Intent" is not the mental state the laity (i.e., non-lawyers) think it is. Barr knows that, but he's playing on public ignorance of the standards of the law to make those standards impossible to fulfill. Unless, of course, we're talking about punks on the street (usually black, or brown, hem-hem) who are guilty because they are practically born with "criminal minds." But Trump is a rich white man and the POTUS, so he can't be guilty because he's too stupid to know he's committed a crime, so how could he intend to commit a crime? He was just trying to win and election and run a government. How could he know what was legal and what wasn't? He was just an innocent babe in the woods, beset by cruel investigators and obnoxious reporters. Because he was so frustrated by the press coverage of his presidency, he gets "King's X," right?
This is bullshit. Even William Barr couldn't construct a 19 page legal memo on these premises.*
When even Chris Wallace can see it, you know it's as plain as a poker:
“When it came to the obstruction case, there were 10 instances that the special counsel raised that could be considered potential obstruction, then you got into this very curious area where the attorney general seemed almost to be acting as the counselor for the defense, the counselor for the president rather than the attorney general — talking about his motives, talking about his anger, his feeling this was unfair and there were leaks.”
“And really, as I say, making a case for the president. I suspect the Democrats’ heads on Capitol Hill were exploding and they are going to come down very sharply about the way that Bill Barr today laid this out… this is the first look in a sense that everybody has gotten today at the Mueller report and this was as good a case as the president and the president’s lawyers could make that there is nothing to see here, let’s move on,”
Or just walk away, whichever's easier:
Why Bill Barr's press conference was a farce, in one moment https://t.co/1re7uu44TY— Aaron Rupar (@atrupar) April 18, 2019
Further to the point:
Toobin on CNN: "The idea that being frustrated by leaks is exculpatory is exactly backward...A concern about leaks and response to them can be evidence of criminal intent. That’s what it was in Watergate."— Michael M. Grynbaum (@grynbaum) April 18, 2019
*First report on the actual Mueller Report is that the Special Counsel found 10 incidents where Trump obstructed justice. Barr just disagrees with Mueller's legal theories, and declares the President not only "not guilty," but innocent as a lamb.