"Democrats" aren't a monolithic block, even if leaders of the Democratic Party (and enemies of the DP) may want us to think this.
So probably no one can say why "Democrats" are against the wall, because it's likely they have several different but overlapping reasons.
Based on the Democrat I know personally, I think many of them come from immigrant families, and their grandparents were hugely grateful to be able to enter the United State after fleeing from political persecution, religious persecution, and poverty & war in their countries of origin.
To Democrats of this kind, the Statue of Liberty is the emblem of the very best American traditions and values, and Trump's wall stands for almost exactly the opposite values. Democrats of this kind seem to believe that they're upholding the best traditions of "Americanism," and they see Trump as upholding the worst.
I think SOME Democrats --- like some wealthy Republican business owners and corporate executives -- really believe in "open borders" partly because they seem to symbolize individual liberty, partly because they serve capitalist business interests. They mean US cotton producers, vegetable growers, meatpacking plants and restaurants -- not to mention Silicon Valley tech companies -- will always have a big pool of cheap or at least competitively priced labor to hire.
Some Democrats are strongly opposed to white racism and racial hatred, and they see Trump's border wall as a symbol of a basically racist approach to immigration policy, one that's designed to keep nonwhite people out of the country so that white people born in the US don't feel uncomfortable.
And I think many Democrats -- although I can't speak for anyone but myself -- see Trump using the wall as a political prop with his base, and using rhetoric about the wall to whip up racial fears and racial hatreds in this country for his own political advantage. They see him using racial fear and xenophobic fears of foreigners as a weapon both against liberal Democrats and against older, more conventional business-friendly Republicans.
-- democratic socialist