Explanation:
I'm not sure there is any direct evidence that it was strategically a bad idea. Strategically it made sense to attack the Soviet Union while they were weak and unprepared for war. Hitler knew that as he made progress on the Western front that Stalin grew more and more nervous every day about the growing power of Nazi Germany.
What must be remembered is that Hitler almost won the war with the Soviet Union. Hitler felt the army was not moving fast enough towards Moscow. If Hitler's commanders had done what Hitler had wanted, which was rush as fast to Moscow as possible, then it is possible the Soviet Union would have fallen without time to prepare a massive infantry army. Germany's army was also not prepared for fighting in cold weather. It was not expected that the Soviet Union was even close to capable of fighting back. The Soviet Union's army was in shambles throughout the entire war. It was ill-equipped and all it had to offer was quantity over quality.
The combination of the cold, unexpected resistance and the amount of time it was taking to get to Moscow because of cold weather and resistance was setting back Germany. The whole strategy was to get in and occupy Moscow and take the leadership. It took about six months for the Germans to get nearly to the gates of Moscow, when the tide finally started to turn at Stalingrad. Hitler most importantly underestimated the sheer will of the the country to defend itself no matter how much the cost in blood. The Soviet Union lost a whopping 13.5% of its population to the war.
So in short, strategically a lot of it made sense at the time. The operation was blundered because the blitzkrieg was not fast enough, the underestimation of the kind of force the Soviet Union could pull together and an underestimation of the cold winter. The plan was also delayed because of setbacks in the Balkans and helping the Italians out where they had failed.
It's hard to find actual strategic proof of what was going on through Hitler's mind and his advisors to take on this risky operation. We do know however that these had been a part of Hitler's plans for years. In my opinion, it was probably thought at the time the odds were in Nazi Germany's favor. In all reality, the Germans had a pretty good chance of winning the war within six months, perhaps if just a few variables had changed they might have actually pulled it off. If they could have gotten there a month earlier, they probably would have won.
Also Great Britain was absolutely in no position to put up any kind of resistance except for the occasional bombing run, which was producing much larger losses than they could keep up with equipment wise.
Also Stalin and Hitler were not real allies, they only had a non-aggression pact, and both were not exactly known to be trustworthy. Stalin was also at many times gullible and Hitler took advantage of this diplomatically. Even when warned that Germany was going to invade, Stalin dismissed his advisers.
Taking in all these factors, the thought probably never occurred to Hitler and his officers that the Soviet Union would ever be able to launch any kind of counter attack. It took quite some time and the United States to intervene for the Soviet Union to really begin its successful counter-offensive.