He did because he could. Constitutionally.
Not every use of military force constitutes a war. From the days of Jefferson and the Barbary pirates onward presidents have employed military force without a declaration of war when necessary to protect US interests and US lives. This is fully constitutional because it is in furtherence of the president's express and implied duties as chief executive and commander-in-chief to protect the US, its people, and its interests. If a president were to abuse this authority he could be impeached.
Placing Clinton's cynical self-serving political agenda aside, his cruise missile attacks on the aspirin factory and deserted terrorist camp were fully constitutional because they were directed at a genuine, real-time, real-world threat that could have been neutralized quickly short of a cumbersome declaration of war. Clinton didn't screw up by bombing these places. He screwed up by employing ineffective, craven, and half-hearted means of getting it done. Had one of those missiles taken out Osama bin Laden I would have been among the first to applaud.