Think of Canada, Australia and New Zealand.
These are all former British colonies in which people of British descent have long been socially, culturally, politically, economically dominant.
Because of the fact that the dominant social group in those countries was of British descent that meant that they spoke English, had similar political and judicial traditions to the UK, viewed British history like the Tudors and the Stuarts as "their history", and felt loyalty and amity with the UK.
But, when non-British European migration started happening to those countries post-WW2 and later Asian, African and Middle Eastern migration, things started to change.
Greek, Polish, Norwegian, Italian, Hungarian, German immigrants and their kids in Canada in the 1950s/60s etc didn't feel the same way about Britain that people of British descent did. They were more invested in their own homelands. They may have spoken English, but they wouldn't call the UK the "mother country" or feel loyalty towards it or view British history as "theirs"; rather they'd have been likely to transmit historical grievances against Britain from their ethnic homeland to Canada. An example is how many Italian and Ukrainian-Canadians in the 1960s were demanding that Canada change its national flag from the old Red Ensign flag which had the Union Jack in the corner because they didn't identify with the UK whereas most British-origin Canadians supported the old flag because they did.
Similarly, French-Canadians were demanding bilingualism in Canada and conducing terrorist actions like blowing up mailboxes which had the word "Royal" on as well as demanding the abolition of the monarchy in Canada since they didn't identify with Britain.
In Australia and New Zealand, people of Irish descent have long been the most ardent republicans since they don't feel an attachment to the UK. And, white people of non-British descent like those of Dutch and Greek descent have also been republicans, tend to be the ones most strongly in favour of Australia changing its national flag to remove the Union Jack, and tend to have little care for the UK. This is because they are not of British descent so feel no attachment to it.
This fundamentally goes to show that blood is thicker than water.
Australia, Canada and New Zealand were only loyal to Britain and only strongly identified with it because people of British descent dominated those societies and because they are "blood" relations of British people. By contrast, continental Europeans are generally indifferent to, if not hostile to Britain, since they are not "blood" as proven by the actions of their diasporas like Greek-Australians demanding Britain gives the Elgin Marbles to Greece, thus showing a pro-Greek not pro-British stance whereas an Anglo-Australian would likely favour Britain; or a Cypriot-Canadian demanding that Britain evacuate its bases on Cyprus, thus favouring the Cypriot/Greek position rather than the British one as an Anglo-Canadian may be inclined to do.
Think also about the Dutch settlers in Soutb Africa causing issues. Their disdain for Britain led them to fight the Boer Wars and push for a South African Republic in 1961.
So, given all of that, why would you want to be part of the EU, which is not just a "trade zone" but an attempt to forge a European superstate? Continental Europeans, as demonstrated by the behaviour of their diasporas in Anglosphere nations, are not "blood" or loyal to Britain in the way people of British ancestry are? They are inclined to follow their own biases and cultures and traditions, which often are opposed to the UK, because they are not "us".
They are and their diasporas are either indifferent, or hostile; but they are definitely not loyal.