The supposed impetus for this was the argument that if 18-year-olds could be drafted to fight in Vietnam, they should be able to vote. But U.S. involvement in that war was already winding down. The draft did not last much longer, and an all-volunteer military has long since proven its merits. The real motive for the amendment was the irresistible temptation to gerrymander the electorate, enlarging it to include a huge cohort of politically mobilized and left-leaning young people to swing the vote toward Democrats. (The immediate result, however, was that these young voters stampeded the Democratic Party into nominating George McGovern, who went down to a crushing defeat in the presidential election of 1972.) To this day, the most reliable left-leaning cohort of the electorate is the 18- to 24-year-olds. The push to let 16-year-olds vote is a transparent attempt to continue this gerrymandering.
The reason the Left wants these young voters is the very same reason they should not be permitted: they are easily influenced and indoctrinated. By necessity, and particularly in our current educational system, students tend to learn things in theory—not just from books, but from carefully selected and sanitized textbooks—rather than from deep research or personal experience. This gives the people who dish out that theory a disproportionate influence. In effect, the call to let 16-year-olds vote is a call to amplify the votes of teachers’ unions. If you think political indoctrination in the schools is bad now, wait until it has the direct power to tip election results.