Initially, it could have been the plan. Generally, if the South had wanted to win the war, all they had to do was simply stop their forces being crushed. To paraphrase Jay Sexton: if the North wanted to win the war, they had to win; if the South wanted to win the war, all they had to do was not lose. That is to say that the Confederates simply had to outlast the Union forces until it became too costly for the Union to continue - in many ways much the same war of attrition fought by Washington, made theoretically easier by it being fought across a much larger stage than the thirteen original colonies.

So what changed? Why did reasonable men and strong commanders, who knew that this was their simple goal, choose instead to take greater risks and follow seemingly-illogical strategies?

In the first instance, the Battle of Manassas (First Bull Run) should be looked at for its psychological effects on the military leadership in the War. Essentially, the early confidence-boost it gave to the Confederates made them believe that the "hunker down and wait it out" plan wasn't necessary - and that they could just do this as a series of pitched battles.

Secondly, consider the distribution of Confederate forces. In an ideal world, they'd have been almost entirely focused around the Northern Virginia area and the Shenandoah Valley; while protecting Richmond in 1861-2 wasn't as critically important as it ended up becoming three years later, that was still the point where the Union was most likely to enter - better defences on the coast could have stunted McClellan's Peninsula Campaign as well. However, this ideal did not come to pass due to massive public pressure from Confederate citizens - they demanded security and protection on every single piece of border, regardless of how tactically-sound that might have been.

The result of the latter point was that instead of being a localised, well-fortified force based mostly around the defence of Virginia (which could have turned every battle into a Fort Wagner and stymied Union forces), the Confederate armies were spread thinly across masses of border. This meant that strong defence against greater numbers was less feasible, and so the notion of constant movement and momentum gained credence.

There's also much to be said for the experience of Lee's forces in the Peninsula Campaign. Once Lee renounced his "King of Spades" title in favour of getting out of the trenches and really abusing the vulnerabilities in McClellan's momentum (which had been lost just before Richmond), his 2nd Army undid a campaign's worth of work in the space of the Seven-Day Offensive. With that kind of great success clearly visible, who can blame commanders for wishing to continue that kind of push? Of course, perhaps the exact details of the Union delay were not properly understood by those wishing to imitate the success of the Seven-Day, and so the offensive strategy mostly fell short of what it was truly capable of achieving when applied properly.

Main source for this is McPherson, Battle Cry of Freedom