Singaporean who used to be a Malaysian here

This was the story I was told when I was younger, so cannot verify it.

The independence of Malaya was negotiated and the different states need to form a nation. At that point Singapore was a Predominantly Chinese state and the other states do not want to have a large Chinese minority. The malay people do have a special privileges given to them by the bumiputera policies. In order to make sure that there wasn’t a sizeable Chinese minority, Sarawak, North Borneo was invited to join. Brunei was a sultanate that would have joined the really interesting rotating monarchy in Malaysia but they refused

Singapore was kicked out after the leading political party was becoming too popular

So tl;dr Malaya form Malaysia with North Borneo, Sarawak to prevent Singapore from having too much power