Because that's the most efficient thing they can do at that time.

Japanese pilot training program is pretty poor, not so much that it produce low skill pilot, far from it, but in that there's no real equivalent of systematic rotation of skilled pilots back from the frontline to serve as veteran instructors to new pilots like on the Allies' side, so very low skill transfer happens because those pilots would just die in the frontline. Combining with the low graduation rate due to their big emphasis on quality over quantity means that the Japanese just cannot scale up pilot training like they can scale up plane production without pilots' quality suffering. This combining with increasing AA and fighter proficiency due to better technologies and training (including the veteran instructors) on the Allies' side eventually leads to the Marianas Turkey Shoot which badly damaged the Japanese naval air arms. It's also not helped that the Japanese tried to keep several of their best pilots in order to deploy them on some decisive battles so the active pilots end up suffering more when the aces aren't deployed.

So the Japanese had to think of the ways to make more efficient use of their resource to damage enemy ships, and using suicide planes is great for this. This is best illustrated in the US Antiaircraft Action Summary, namely the Suicide vs Conventional attack table:

TABLE I

Bombing And Torpedo Attacks

300 planes sortie

180 lost to CAP (60%)

120 attack ships

40 lost to AA. (33.3%)

12 get hits or damaging misses on ships (10%)

80 return to base

220 lost to CAP and AA. to score 12 hits.

TABLE II

Suicide Attacks

60 planes sortie

36 lost to CAP (60%)

24 attack ships

12 lost to AA. (50%)

12 get hits on ships (50%)

0 return to base

60 lost to score 12 hits.

You can see that under this calculation, the Japanese can use considerably less number of planes to score 12 hits against enemies. The increasing AA effectiveness means that even if conventional attack planes survive, the AA might scare the attackers enough to ruin their aim anyway, resulting in low hit rate.

There's also several other advantages:

• Kamikaze pilots need much less training than conventional pilots

• They can use planes that are obsolete in conventional dogfights to still do some damage

• They can use their diminishing resource to create a less resource intensive suicidal planes for that one single job, including things like human-guided missile like the MXY-7 Ohka

• It's technically harder to destroy Kamikaze planes, because you not only need to shoot the plane down, you need to damage it enough that it'll be destroyed before it hits the ship. The fate of the USS William D Porter can also show how luck can make things better for kamikaze plane that wasn't thoroughly destroyed to hurt the target ship, namely that plane crashed into the sea, but retained momentum to travel under the destroyer, THEN explode, eventually causing the ship to sink.

• Since you're going to crash into the target anyway, you don't need to slow down, thus making it harder for the target to hit you back, while dive bombers have to pull up, and torpedo bombers have to fly slow and level before deploying torpedoes.

Still kinda hope that more experienced redditors can expand on this though, since I'm not the best at explaining this.

Sources:

Norman Friedman - Naval Anti-Aircraft Guns and Gunnery

Parshall, Tully - Shattered Sword

http://pwencycl.kgbudge.com/F/i/Fighter_Pilots.htm

http://www.ibiblio.org/hyperwar/USN/rep/Kamikaze/AAA-Summary/AAA-Summary-1.html

To put it bluntly, the Japanese felt that very desperate times called for very desperate measures. Keep in mind that there was really no such thing as real "precision guided ordnance", or "smart bombs" back then in WWII. Kamikaze pilots were essentially introduced and implemented by the Japanese to try to fill that role, creating human-guided precision cruise missiles out of their aircraft that were deemed to have a much better level of targeting accuracy, or CEP (Circular Error Probability) than the unguided bombs or torpedoes of the era could provide, particularly against constantly moving and maneuvering targets like those which US and allied surface ships presented.

A Kamikaze pilot could literally guide and fly their plane all the way directly to the point of impact with the target, believed to ensure a higher hit ratio than merely dropping "dumb" bombs had proven to provide. When Japan implemented the Kamikaze program during the latter stages of WWII, they were already "on the ropes" and getting their butts kicked pretty good in the Pacific naval theater, and they needed a method of trying to ensure a higher hit rate against the largest and most threatening of American naval vessels (aircraft carriers and battleships in particular), and since the level of technology of the day did not allow for guided bombs, missiles, or torpedoes to be employed with any real success, the next best option was felt to use live men as the onboard guidance system, having those pilots literally commit suicide by being ordered to fly their aircraft at high speed directly into those surface vessels in order to cause the most damage.

The Japanese code of Bushido made this, what in their eyes, was deemed a practical option, and that Bushido code of honor made it difficult for pilots selected for or who initially volunteered for the program to back out later. Though this style of suicidal combat would mean the Japanese would assuredly lose both an aircraft and a pilot during the attack endeavor, that was deemed a necessary concession or worthwhile loss given how the American naval juggernaut was tightening the noose and closing in on the Japanese Island chain. Kamikaze-style attacks were very much a last ditch effort by the Japanese to try to halt, or at least slow, the American naval advance for a period. It was inefficient, but was deemed to have a chance of being more effective at causing damage than trying to just utilize mere "dumb bombs" dropped from "on high" or low level strafing runs to attack the US Pacific fleet.

Well, as it goes, one airplane trying to take on an entire ship isn't horribly effective, but one ship rigged with explosives is another affair entirely. Making imprecise weapons like bombs and torpedoes hit a ship while being fired upon is difficult, especially when your goal is to hit something important like a munitions magazine instead of simply ripping a hole in it.

First thing you gotta remember is that the wasn't merely a strategic initiative but also a psychological one. A fairly common assumption that most of the Axis powers took for granted, especially with regard to the US, was that the allies had no stomach for a long, protracted war. Germany had gotten drunk off it's success in defeating neighboring countries with smaller, often obsolete armies and aged WW1 era equipment. The Japanese had gotten confident from their success in China, the Philippines and the rest of the southern Pacific. Kamikaze maneuvers were designed with the intent to both break the spirit of the American forces as well as making the best of their strategic situation. It's a lot easier to put aircraft in the air when you're not concerned with return trips, and Japan was not ignorant of public opinion in the US with regards to the course of the war. Spending months and tens of thousands of lives to take one dinky island in the Pacific with little to it's credit besides monsoon rains, rocks, jungles, mosquitoes and malaria wasn't a good look, especially with it becoming rapidly clear that the chickens were coming to roost in Germany, and they were some fat, hungry birds.

Second thing you gotta remember is that aircraft- like all machinery- wasn't as simple as slapping parts together. Build the aircraft and you still need to stock it with bombs and munitions- by the end of the war Japan was going back to training civilians in the use of bamboo spears and drilling them on formations and making earthenware (the type 4) grenades. You still need to put fuel in your aircraft. You still need trained pilots. Where the western allies had the luxury of training pilots and retiring pilots who have flown a given number of sorties to train the newbies, Japan had no such luxury. They eventually did reach a point where the choice was between training new pilots or keeping the ones they already had in the air.

And eventually they also reached a point where come 1945 Japan was throwing it's entire fleet at the US advance hoping that something like the Yamato- which had been dispatched with orders to eventually beach itself on Okinawa and to fight to the death- could at least blunt the Allied advance. If the Japanese empire was willing to send their prize battleship with 2700 crewmen out to die on a one-way-trip it's not exactly difficult to appreciate that they'd be willing to send a small fleet of aircraft to their deaths as well.

Seems inefficient at best

To be succinct, inefficient methods still worked where something ideal- or at least something akin to what the Americans or the Commonwealth would do where if you fly enough missions, fight enough enemy pilots, you got benched- was no longer viable due to Japan's strategic situation. Even before the Americans started planning for an unthinkable land war on the Japanese mainland they'd effectively crushed Japan's navy, and sea trade was all but stopped. At that stage Japan didn't even have the means to feed it's own people, never mind having the resources to build, supply, and fuel aircraft to then train pilots. But they did have aircraft. Where Germany had been forced into building the ME262 because it was much more tolerant of ersatz materials than a traditional piston engine aircraft- even if it was wildly unreliable, and was incredibly slow to accelerate, making them sitting ducks as they took off and got to altitude- and used a unique fuel source that simply couldn't be used to run, say, tanks, Japan was using the aircraft they had available to make the best use of their strategic situation.