I don't know how you can say this without addressing the very real history of segregation in this country as a key factor.
Why are you changing the topic from description of the rate of cohabitation to explanations for the phenomenon? My statements were correct.
Since you insist: there are over 200 nations in the world. Other than Singapore (forced cohabitation between Chinese and Indians), which nations have higher rates of cohabitation than the US? If you can't think of many, could it be that the legacy of legal segregation is not the main factor?
Suburbs were specifically designed to be racially segregated enclaves for whites
There was no central planner. Whites chose to move away from riots and crime in the inner cities. As the map I posted above shows, the races still aren't cohabiting for the most part, even in the inner cities. They form islands of one race, with a few exceptions.
Besides, you're insisting on a narrow definition of cohabitation
True, but it's also the most fundamental definition: who do people choose to live with and make families with? Unless something has changed radically in the past few years, the answer is clear:
How can you say that living in multicultural city doesn't count as cohabitation?
Because that’s not the definition of the term, and it’s not how the term is typically used. Here are the relevant definitions from Merriam Webster (I removed a third definition for being irrelevant):
1 : to live together as or as if a married couple
• They cohabited in a small apartment.
2 : to live together or in company
• buffaloes cohabiting with crossbred cows
• —Biol. Abstracts
In any major city people spend much of their time outside their neighborhoods and interacting with people of other neighborhoods
I wonder why most of them don’t choose to cohabit with people of other races though.
The politician quoted in the OP explicitly mentions society in her answer, in America we very much live in a multicultural society even if some of our neighborhoods aren't.
She mentioned cohabitation within a multi-cultural society. She argues that it doesn’t work out. Ours is certainly a multi-cultural society, but there is not much cohabitation of different races. Therefore the US is not a counter-example to her statement.