Let's look at some of the things that might go wrong because of bad selection of a control group. What things might lead us to mistakenly conclude that radishes prevent tooth decay when they really do not?
Suppose the people in the control group were recruited separately, say at a different college. Perhaps the people going to that college had more cavities on the average than people at the college where group R was recruited. This might be because of a difference in the cafeterias or water supply at each location or because of differences in rules regarding alcoholic beverages or differences in the backgrounds of the students who attend each college. In any case, if group R had fewer cavities, it may be because of differences in the two groups other than the fact that group R ate the radishes. This spoils the reliability of the experiment.
Good researchers try to eliminate any factors that would tend to make the control group different from the test group. They would not, for example, take the first 10 volunteers as group R and the next ten as group X, for fear that some factor that affected when volunteers arrived also would affect their tooth decay rate (perhaps the people who arrived earlier were more likely to have skipped breakfast). The proper way to assign people to groups is to first choose all the people who will participate and then use a random method to determine who goes into each group.