Many people believe that too much immigration causes the destruction of a nation or of an ethnic group by means such as the disintegration of its political and social institutions, of its culture, language, national feelings, religion, and its economic existence.

If immigration leads to more unemployment, then that is an economic problem, especially in the hypothetical case where the social benefits system is getting more and more strained by an influx of unemployed people. But generally, I think that you can expect that the immigrants will soon find employment. Besides that, there's the cultural aspect that @jet@hackertalks.com mentioned. You could also make the point that the country's infrastructure is more and more stressed as the population grows, but that is fixable and potentially counteracted by the labour potential of the immigrants themselves (i.e., qualified immigrant work forces can make a large-scale infrastructure overhaul possible that will lead to greater national capacities and a net benefit for the entire population).

Aside from these things, I would argue that most of the other reasons boil down to xenophobia or racism.

Infrastructure is a large issue. Border towns can become saturated, which will reduce living conditions, and when immigrants move to larger cities, they can often have trouble finding places to live. A lot of this can be because of a communication barrier. Sometimes that is because there are too few to translate, but there can also be educational issues. As much maligned as the US education system is, it is better than some others, and when your culture eschews school for an early start at earning a paycheck, communication in any language becomes a challenge.

Many issues can be overcome, or at least minimized, by compassionate workers, which many that work with immigrants are, but there isn't enough funding to get compassionate people where they are most needed. Supporting increased budgets at the border isn't always about putting guns on the border, it can be about improving the infrastructure that helps get people where they need to be in more efficient ways. I'm starting to ramble, though, and I think I've given a partial answer to your question.

Many companies love undocumented workers. Easy to abuse, underpay, overwork. So of course they hate it when those workers can easily get documented or citizenship. Following the law is such an annoyance. Cuts into the profit margin. That is why big business and the nationalists often work together.

The nationalists kinda know they're getting played to generate corporate profits, but they also enjoy having a target to look down on.

Racism