official thinking still being that...

[cannonkuo]

When Perón was elected for the first time in 1946, these dispersed assertions of the Argentine claim were merely mentioned more often, official thinking still being that the 'Malvinas' would eventually be Argentine.
(Argentine Approaches to the Falklands/Malvinas: Was the Resort to Violence Foreseeable?)

May I know why being is used instead of "was" in the sentence?

 

[Tarheel]

Keeping in mind that it's all one sentence, why would you use "was" there?

("May I know " is very formal and rarely if ever used by native speakers.)

 

[emsr2d2]

With the word order the writer chose, "was" wouldn't work because it doesn't fit after "still". It could be written two ways:

... official thinking still being that ...
... official thinking was still that ...

As you can see, the position of "still" is different. Your final question would be more natural as "Can you/someone tell me why ...?" As Tarheel said, "May I know" sounds odd and old-fashioned to native speakers.