Why did the Japanese attack the Aleutians at the same time as Midway?

I think each answer so far has hit on very important points: complexity of Japanese planning, diversionary tactics, and Army-Navy rivalry. One thing I would like to point out, however, is why Midway was such as a success and why the Aleutians diversion failed.

We had partially broken the Japanese naval codes in use at the time and the Japanese were unaware we had this ability. We, the US, was fairly certain the Japanese would try to gain a major strategic advantage in the summer of 1942, but there were no clear cut answers as to where they might strike. The Japanese defeat at the Coral Sea forced them to shift their thinking. Capturing Midway would directly threaten U.S. Pacific forces at Pearl Harbor and might just give them the ability to claim the Pacific as their own and prevent us from approaching their imperial holdings in China, the Dutch East Indies and Southeast Asia.

Anyway, back to the naval codes. We knew shortly before the attack that the Japanese had settled on Midway Island as their target. Had we not known this, the attacks on the Aleutian Island chain might have been provocation enough for our fleet to head north and miss the decisive strike entirely. But U.S. military planners, however, had a fairly complete picture of Japanese intentions and so, didn't fall for the bait. Instead we concentrated our forces at Midway, not as a lucky guess, but knowing full well what was coming for them.

I did watch a Youtube about the Coral Sea battle and, yes, it seems that Japanese Navy loved complex plans with lots of different forces. And, yes, what might seem natural to Westerners raised on Clausewitz and Napoleon - pushing for a decisive battle with all your forces - may not be as appealing to Japanese, especially if someone like Sun Tzu was an influence.

But I still utterly fail to understand why the Aleutians couldn't wait until after Midway.

I would like to quote an English source, but unfortunately, the Wiki about the wars toward Aleutians in English is so poor, thus I would like to quote the Japanese wiki.

アリューシャン列島は、太平洋戦争開戦時の連合艦隊作戦計画では占領または攻撃破壊すべき外郭要地として定められていたが、これは十分検討を経て決められたものではなかった。その目的は、アメリカの北方路の進行を阻止するもので、米ソ間の連絡を妨害し、シベリアに米航空部隊が進出するのを妨害しようとするものであった。日本本土の東方海面は幅広く開放されており、米空母の本土への奇襲を防止するには、莫大な哨戒兵力が必要であったが、海軍はこれに十分な兵力をさく余裕はなく一部を重点的に哨戒する他なかった。その状況にこの正面の警戒を担当する北方部隊は不安を抱いており、特に米空母の機動が開始されてからは、一層その不安がつのっていた。

Translated

Aleutian archipelago was set according to the plan by the Imperial Japanese combined fleet as the important factor either to be attacked or occupied, but the process ( or the goal ) of the plan was not satifactorily planned in detail at the time of the opening of the war. The direct purpose of the rough plan was for the JIA to shut down the American fleets to advance to northern area, particularly ( by the JIA ) focusing to disrupt the communication between the U.S and the Soviet. The JIA's north eastern territorial sea field was too vulnerable or too large to the surprise attack by the U.S fleet on the main land Japan ( like doolittle ) but the JIA needed a huge number of armies to defend against this so that the JIA had only choice to pinpoint targets to satisfy this situation. Some division staffs of the JIA's naval fleet whose job was to protect this area was so worried about this situation particularly after the operation by the U.S fleet resumed its operation.

一方で1942年2月、連合艦隊のセイロン島攻略作戦図上演習において米空母の機動に手を焼いたばかりでなく、アリューシャン列島西部のアッツ島に近いセミチ島からアメリカの最新大型爆撃機による帝都空襲が行われ、その一部が奇襲に成功したことで日本の同方面に対する関心はさらに高まった。また米空母の機動が頻繁となり、わが本土奇襲の懸念がますます増加してきた。そのため連合艦隊も軍令部もこの正面に対する関心が強まり、一部にはキスカ攻略の実施を考えるものも出てきていた。このような時期にミッドウェー作戦が内定した。そこで軍令部はミッドウェーと同時にアリューシャン列島西部を攻略し、米航空兵力の西進を押さえるとともに、両地に哨戒兵力を進出させれば、米空母のわが本土近接を一層困難にすることができると判断し、その作戦実施を連合艦隊にはかり、連合艦隊でもその必要性を認めていたし、攻略兵力にも余裕があったので直ちにこれに同意した2。

Translated

On the Feb 1942, Japanese Imperial navy conducted its own tactical map operation to attack Ceylon island, which ended up to invite not only the traumatic ( loss of its own ships or hardship to destroy ) the U.S fleets, but the anticipated air attacks by new bombers ( if this description is addressing either about B-19 or B-29 is unknown ( by me. )) on its own empire's homeland from Semichi? island near Ats island which is located at the southern part of the Aleutian archipelago and the result of the tactical map operation ended up that U.S ( new ) bombers could've attacked Japanese main homeland. Under this circumstances staffs of the Japanese Imperial Naval combined fleets became strongly concerned about those areas, and one of staffs strongly started to demand the attack and the occupation of the Kiska island. At the same time, the Operation Midway officially started. Under such time, the Imperial Japanese Navy's command department drafted a tactic : Attacking the Midway but also advancing to the western parts of Aleutian archipelago to set up the bas*m*nt for the patrolling, which potentially could have stopped the advancement by the U.S fleet from this side, and could've delayed the potential areal attack from the north, and this draft was accepted by top of the Japanese Imperial Naval combined fleet, which also foresaw the danger from the north. I will skip some part, since the conclusion will be same anyway.

1942年4月15日（推定）に上奏された「大東亜戦争第二段作戦帝国海軍作戦計画」には、「成る可く速やかに「アリューシャン」群島の作戦基地ヲ破壊又は攻略し米国の北太平洋よりする作戦企図を封止す」とある[6]。

Translated,

On the military draft by the JIA army on the estimated 15h April in 1942, named "The Second stage of the Japanese Imperial Navy's operation on this war" says, "As soon as possible, we need to either destroy or occupy the U.S bas*m*nt at the islands of Aleutian archipelago so that we stop the attack by the U.S from the North.

Conclusion

Now, in wars, concentration of forces is generally considered a good thing.

Yes, but unfortunately? It didn't or couldn't apply to the JIA's Navy.

But there are valid reasons for splitting up an attacking force: a diversion to lure defenders elsewhere, a simultaneous attack to force the defenders to split up their forces and finally increased opportunity for flanking the enemy when your forces are not too widely separated.

As I presented above, ( it seems to cover the whole Pacific ocean by its own navy ( Attack on homeland by the U.S fleets was considered to be "at the time" was "inconsiderable" ) was "too stretched" ), and the Japanese Imperial Army "at that time" considered the attack from the north by the U.S as a great potential threat to its own homeland. And they ( JIA ) took it seriously. But it seems they had no choice, so that they went on to the Aleutian operation despite Midway.

With 20/20 hindsight you can win just about any battle. Which is what we do here in this question. Military History Visualized has a good explanation. Japanese operations were usually quite complicated. This was no exception. Had Yamamoto been replaced by another admiral, the plan would have been just as complicated.

To elaborate on that: Yamamoto directed the planning and operation. He didn't do it alone, his staff was working out the details. Replacing Yamamoto with any other admiral would have presented a very similar (and complicated) plan.

They thought they had destroyed a carrier in the battle of the Coral Sea. However, the USS Yorktown was quickly repaired and send into action. That was one carrier the Japanese didn't think to be there, and gave the US 50% more carrier power.

And lastly, in war everybody makes mistakes. The Japanese had the bad luck in this battle that everything they did wrong worked against them, likewise the US Navy had the good luck their mistakes worked in their favor.