Williamson gave SSPX a reason to kick him out.

Actually, he has been doing that for quite a while now.

Because as far as he is concerned, Bishop Richard Williamson thinks that he is the ONLY CATHOLIC BISHOP walking God's green earth.

Now here is something that would, I think, put the proverbial "nail on the coffin" for this hard headed old man.

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Bishop Richard Williamson of the traditionalist Society of St Pius X (SSPX) has administered the sacrament of Confirmation to nearly 100 lay Catholics in Brazil without the approval of his own breakaway society. [He thinks he is his own Pope!]
The celebration took place in Nova Friburgo town, Rio de Janeiro state, at the end of August and was organised by the Benedictine Monastery of the Holy Cross.
On the SSPX's website on 6 September, Fr Christian Bouchacourt, the group's district superior of South America, denounced the bishop's behaviour as "a serious act against the virtue of obedience" and "an attack upon the most elementary demands of courtesy".

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I think Williamson really wanted it this way.

He pushed the envelope far too long.

Give him what he wants.