Which term refers to avoiding making an explicit statement?

The term that refers to avoiding making an explicit statement is "equivocate." When someone equivocates, they use ambiguous language or avoid direct answers to obscure their true intentions or to evade a clear stance on an issue. This behavior can be employed in various contexts, such as politics or debates, where individuals may wish to maintain flexibility or avoid inciting controversy.

In contrast, the other terms involve a more direct approach to communication. To clarify means to make something less confusing or more comprehensible, while to assert means to state a fact or belief confidently. Proclaiming involves announcing something publicly and emphatically, which is the opposite of evading a statement. Thus, equivocate is the most appropriate term in the context of avoiding explicit statements.