The condensation D* of any digraph D has no cycles. It follows from the maximality of strong components that the condensation D* of any digraph D has no cycles.
i'm sorry if this question is silly, but if the condensation of the digraph on the left is the graph on the right then isn't the right graph a cycle? what am i missing here?

 A: In the directed graph setting, cycle means directed cycle. This is stated clearly in G. Chartrand and L. Lesniak's Graphs & Digraphs, third edition, pp. 26–27:

The terms walk, open and closed walk, trail, path, circuit and cycle for graphs have natural counterparts in digraph theory, the important difference being that the directions of the arcs must be followed in each of these walks. In particular, when referring to digraphs, the terms directed path and directed cycle are synonymous with path and cycle.

I understand that you are reading Frank Harary's Graph Theory. Harary is not quite so explicit on this point, but he is using the terms the same way. Quoting from the bottom of p. 198:

A (directed) walk in a digraph is an alternating sequence of points and arcs, $v_0,\ x_1,\ v_1,\ \cdots,\ x_n,\  v_n$ in which each arc $x_i$ is $v_{i-1}v_i.$ [. . .] A path is a walk in which all points are distinct; a cycle is a nontrivial closed walk with all points distinct (except the first and last).

The parentheses in the expression "(directed) walk" tell us that the adjective "directed" may be omitted without changing the meaning; i.e., in a digraph, "walk" means "directed walk". Then a cycle is a walk (i.e., a directed walk) which is closed and does not repeat points; in other words, it is a directed cycle.
The statement about condensations that you are asking about is correct if (and only if) you understand "cycle" to mean "directed cycle".
A: The definition of strong connectivity only "sees" directed edges, so this statement can only be true for directed cycles.
