I'd say that this order was prescribed by The Da Vinci Code's (the book's) high success. While Dan Brown might have been regarded as a best-selling author even before The Da Vinci Code, this book was a major success world-wide and gathered an attention much higher than Angles & Demons or any of his previous books did, I think. So it was just a matter of time till it got turned into a movie. And only later after a whole bigger crowd had noticed Dan Brown and after the Da Vinci Code movie was a big success, too, they are catching up on Robert Langdon's previous adventures. Wikipedia seems to support this to some degree:
In 2003, Sony acquired the film rights to Angels & Demons along with
The Da Vinci Code in a deal with author Dan Brown. [...] Director
Ron Howard chose to treat Angels & Demons as a sequel to the previous
film, rather than a prequel, since many had read the novel after The
Da Vinci Code. He liked the idea that Langdon had been through one
adventure and become a more confident character. Howard was also more
comfortable taking liberties in adapting the story because the novel
is less popular than The Da Vinci Code.
But as to why The Lost Symbol was skipped for the movies, I don't have as obvious a theory, yet. Maybe it was to profit from the temporal adjacency to Inferno's publication or maybe The Lost Symbol didn't sell too well (though that doesn't seem the case). But given the summaries on Wikipedia, it may also be that they wanted to continue Robert Langdon's travel through the Old World and Renaissance history as in the previous movies, which Inferno seems to be pretty in line with. The Lost Symbol seems to tread quite a different path, having him on a chase through American history and Freemasonry in Washington D.C., a path that the National Treasure franchise already went rather successfully.
It also seems, that they indeed wanted to do The Lost Symbol after Angles & Demons, but changed their mind when Inferno was released in mid-2013. There were also issues with Ron Howard opting out for the supposed The Lost Symbol but rejoining when the plan switched to Inferno (along with screenwriter David Koepp?), so maybe that was a factor, too, as can be read here:
Tom Hanks and Ron Howard, the star and director, respectively, of
Sony’s first two tentpole movies based on Dan Brown’s novels, are
returning for Inferno, we’ve learned. Hanks had been expected to
reprise his role as Harvard symbologist Robert Langdon for The Lost
Symbol, the third novel in Brown’s book series. But Howard had bowed
out of that project, which is now on the back burner, saying he wanted
to produce it with Brian Grazer and their Imagine Entertainment but
not direct. Now we’re hearing he’ll return for Inferno.
PREVIOUS BREAKING…Inferno was released in May and is the fourth Robert
Langdon book written by The Da Vinci Code and Angels & Demons author
Dan Brown. Sony, which has film rights to the franchise, has just set
a December 18, 2015 release date for it. David Koepp, who wrote Angels
& Demons, is aboard to write the script. The news means Brown’s third
installment of the thriller series, The Lost Symbol, will not be the
next movie for Sony. Danny Strong had been set to write that
adaptation in March 2012 and the expectation was the film would be
directed by Mark Romanek after Ron Howard opted out of directing as he
had done on the first two pics. Not much has been heard of that
project since, and now Sony is leapfrogging it for Inferno.