why is mr birling particulary pleased to be celebrating sheilas and geralds engagement

Arthur says this is one of the happiest nights of his life, though he is sorry that Sir George and Lady Croft (whose forename he appears to have forgotten) cannot join this “quiet little family party.” Birling tells Gerald that he is “just the kind of son-in-law I always wanted” and that Gerald and Sheila will make each other happy. He also makes clear, none too subtly, that he has ambitions for Crofts Limited and Birling and Company (the smaller of the two firms), though they are currently competitors, to work together at some point in the future, as a result of this marriage.

In order for them to do business together and avoid any competition between them.