Seeing as no-one else has answered yet.

Moltke wanted to outflank and envelop the French forces, and while the Second Army was headed towards Paris, that was not the objective. He ordered Kluck to advance to the south-east to protect Bulow's flank as he pursued the French (this was a turn Kluck had already begun). Thanks to the state of communications at the time, Moltke cultivated a devolved leadership style, making a blessing from a curse, and freely delegated to Kluck and Bulow concerning the pursuit. Until the 29th of August, Kluck was under Bulow's orders, but then he was released from them, leaving neither Moltke, Bulow, or Kluck in charge overall on the right. This caused a few problems. Bulow was cautious and pessimistic, Kluck was not.

Kluck/Moltke's priority at this point was attempting to envelop a great deal of the French forces, namely the First, Second, Third, Fourth, Fifth, and Ninth Armies. The German Second, Third and Fifth Armies were to turn south early, instead of circling Paris, and drive the French forces in a south-easterly direction, away from Paris. Kluck's First Army was to provide flank security. He was not pleased with this role, and pushed on, disregarding the risk. In his own words:

"The message of the Supreme Command, in accordance with which the First Army was to follow in echelon behind the Second, could not be carried out under the circumstances. The intention to force the enemy away from Paris in a south-easterly direction was only practicable by advancing the First Army."

Kluck was proud of what he and his men had done. The Schlieffen-Moltke plan was extremely demanding of the right wing of the German forces, some troops had marched more than 300 miles in a single month, and they had fought hard. Kluck did not wish to be relegated to a supporting role in the German victory.

I suggest that von Kluck was not in fact experienced at maneuvering army-sized formations on actual roads while in contact with genuine enemies who shot real bullets; for the good and simple reason that nobody was. There hadn't been a large-scale European war since 1870; von Kluck had fought in it, but as a junior officer. (And even so, it hadn't been on the scale of the Great War.) The General Staff system in Germany produced good peacetime generals, probably better than the French or British and certainly way better than the Americans or Russians; but there's still a difference between paper maneuvers, staff rides, and even divisional exercises, and actual war with the entire mobilised manpower pool of Imperial Germany. Calling von Kluck 'experienced', then, is a bit misleading; he was an experienced officer, but not at the job he was doing in August 1914.

As for obviousness, everything is obvious in hindsight when you can examine the exact positions of everything!

My understanding is that von Kluck (and the German forces as a whole) were attempting to encircle the French forces. The means they needed to bypass them, so turned away from Paris.

An envelopment is tricky, especially at this scale, and more or less necessitates exposing your flank to the enemy as you pass by them. Von Kluck actually did a pretty decent job of recovering - the pull back was ordered after most of the fighting was over. I'd argue that it was lack of communications, not von Kluck himself that created the pull back. You could also blame Moltke for weakening the right flank by changing the Schleiffen plan.

It could very easily have gone the other way.