Why I Chose to Climb Mt. Rainier
Oh sure, I think there's always a little bit of ... "Because it's there"  in the reasons for someone climbing something, but there's often a little bit more to it.  Here's a bit more of my story behind the story.
Needed Something to Drive Me
Ouch!  Ouch!  Ouch!
In late July 2005, I was on a high coming off the 6 day mountaineering trip and climbing Mt. Baker. However, from August - October, I had the misfortune to experience 3 injuries in a short time period.  I got a slight bone bruise/stress fracture? in my right foot, suffered an injury to my back (somehow), and then managed to unwittingly pull/strain my rhomboid muscles on the left side of my back.  I figure I lost about 85% of my strength in my upper shoulder, left arm/wrist from the rhomboid injury. 
What? Why?    "Because It's There..."
For a highly active guy like me used to running 15-20/miles per week, my devastated fitness from these injuries and their pains was truly demoralizing.  I knew it was going to be a long, slow road back to recovery and that I needed a good challenge to help focus my mental and physical energies day after day.  But setting my sights on a 10K or half marathon was not feasible. So, what could I...
Certainly, 'Because It's There"... that's part of it.  If you've been in or flown to Seattle, and had the fortune of clear weather, you can see Mt. Rainier - rising up, massive, awe inspiring.  You definitely feel an urge to pursue its challenge - "because it's there".  Any hiker or mountain climber worth his/her boots is probably going to have a little of that in them. 
Deciding to Do Mountaineering Stuff
I started mountaineering in 2005. One of my primary reasons for doing AAI's 6 Day Mountaineering School, besides my general interest, was that I had injured my calf while training for the '04 Dallas Marathon after completing the '03 Chicago Marathon.  I didn't think that my running form would return in a hurry, so instead of a marathon race goal, I decided to "step up to the next level" and learn some mountaineering instead of the usual Colorado 14'er hiking I do in the summer.
Hmmm...    let's see,  I think I'll sign up to climb Mt. Rainier!
For me, there were some other logical reasons in additional to the traditional climber mentality.
First, there are lots of glaciated peaks in Washington, but none like Mt. Rainier, the highest peak in the Cascade Range.  After considering some other alternatives, I still wanted to go for the highest mountain.  Sometimes you never know when you will get another chance to do something.
Second, climbing Mt. Rainier represents the 'next step' in a logical, sequential progression of doing higher climbs with Alpine Ascents, Int'l.  I have a long range goal to eventually climb 1 or 2 of the "7 Summits" (Elbrus, or Aconcagua) and one needs to take on higher mountains / altitudes to develop experience for these peaks.
So, in summary, I chose to climb Mt. Rainier, not only because of its magnificence and stature as tallest in the Cascades, but also because it is one step towards a larger goal in the future.
And yes, because it's there!