Should I avoid pairing my opponents first lay in cribbage (singles)?
Let's look at some statistics. Let's assume that you have only a single one of some card value 'x' and 3 other cards. Let's also assume that your opponent has a single one of that card value 'x' (since he laid the first of the 'x' cards). Assuming also that he chose 4 random cards of the 6 he was dealt (not likely, but makes the math simpler), he has 3 chances to have second of that 'x' valued card from a remaining deck of 45 cards (52 - Your 4 - The 2 you threw into the crib - Your opponent's 1 'x' card), 2 of which are value 'x'. The chance of him not getting the 'x' valued card in his 3 more chances is (43/45)*(42/44)*(41/43) or .870 meaning that he has only a 13.0% chance of having a third card of value 'x' and therefore being able to get that 3-of-a-kind. Because you get 2 points for the pair and your opponent gets 6 points (aka you lose 6 points) for the 3-of-a-kind, playing to get the pair nets you (2*.870 - 6*.130) or +.960 points.

If we assume that if he is given a pair of 'x' value cards in his 6 cards, then he will keep them (a reasonable strategy), then the chances of him not getting the 'x' valued card in his now 5 more chances is (43/45)*(42/44)*(41/43)*(40/42)*(39/41) or .788 meaning that he now has a 21.2% chance of having a third card of value 'x' and therefore being able to get that 3-of-a-kind. This nets you +.304 points, a lesser amount than before, but still positive.

In both these scenarios, it is unlikely that your opponent will have that third 'x' card and either way you get a net gain of points over your opponent. Others may have strategies to provide, but these are the raw statistics of your scenario.