ANSWER IN SEVERAL STEPS - long but thorough explanation of what happened and why the trench run was planned
Part 1: The Death Star was designed to be defended from assault by warships
General <PERSON> describes that the Death Star was designed to fight against a direct assault by large warships, they did not figure that small one-manned fighters would be a threat to it.
Most likely the Imperial designers figured that the Rebel warships would attempt to approach the Death Star's superlaser disk cannons from the far side of the station (to avoid being fired upon by the superlaser cannon) and travel in low orbit towards the superlaser cannon where the Rebel warships would use their turbolaser cannons to destroy the superlaser disk cannons. I believe the Imperial designers of the station screwed up with the small thermal exhaust port because they would have focused most of their attention on protecting the superlaser disk from attack by warships that could fire turbolaser blasts at the superlaser cannons on the disk. Also remember that there were multiple exhaust ports, this was a small thermal exhaust port that was below a main exhaust port that did not have any design flaws.
Remember that the Death Star had tractor beams to draw in small starcraft, like it did with the Millenium Falcon. My one question that I would ask is why didn't the Death Star crews use their tractor beams to draw the Rebel starfighters? The most likely answer is that the Death Star crew was caught off guard by a surprise attack by Rebel fighters when the Death Star crew was planning for a direct assault by Rebel warships. The Imperial fighters did not have their crews ready - as <PERSON> orders an Imperial officer to get the crews to their fighters. In real-life battles tactical planning errors can cause disasters in terms of timing - in the real-life attack on Pearl Harbor, the American forces on Hawaii had prepared for sabotage, but not fighter attack, their flak guns couldn't do it, the American fighters were not ready for take-off. The Pearl Harbor example shows how tactical planning errors by defenders cause timing delays, and that can cause catastrophe.
The Imperial officer who tells <PERSON> that the Rebel fighters are so small that they are evading the turbolasers sounds exasperated, because as <PERSON> indicated, the Imperials were expecting a warship assault.
Part 2: Imperial starfighter defense in combination with large number of turbolasers on the Death Star surface pose serious threat to an above-trench attack
As mentioned above, the exasperated Imperial officer who informed <PERSON> of the Rebel fighters evading the turbolasers, appears to have spoken with the turbolaser crews who told him they can't destroy them on their own. <PERSON> however appears calm because he knows that the Death Star has squadrons of fighters to fight the Rebel fighters.
The turbolaser turret fire in combination with Imperial fighter attacks were presumed to be able to destroy the Rebel fighters. 963
But the Rebels prepared for this in two ways:
1) Diversion: The X-Wings and probably a significant number of the Y-Wings created a diversion by drawing in the TIE Fighters to attack them. Meanwhile a group of Y-Wings broke away from the main group and headed for the Exhaust Port. They approached from a distance away, so as not to make their target seem obvious so as to avoid drawing the TIE Fighters after them.
2) Trench: minimal firepower ability by turbolasers and chasing TIE Fighters: By going into the trench, only a few turbolasers could fire at the fighters in the trench, and only a few Imperial fighters could chase directly behind them. Plus the Imperial fighters would be unable to easily chase them from directly behind would need coordination with the turbolaser gunners in the trench to avoid friendly fire as they chased the Rebel fighters. Plus even if the Imperial fighters entered into the trench to chase the Rebel fighters in front of them they would be easy prey for a group of Rebel fighters following behind them.
Part 3: What happened that made the trench run go as it did
Again returning to the conversation between the Imperial officer and <PERSON>. The Imperial officer tells <PERSON> "We count 30 Rebel ships". During the TIE Fighter attack we see that Rebel fighters are being destroyed by the TIE Fighters. By the time of the trench runs by both the Y-Wings and the X-Wings, there appear to be very few Rebel fighters left even though the main TIE Fighter squadron appears to have been destroyed. Also the Rebel fighters do not know about incoming TIE Fighters because the Death Star appears to be jamming signals being emitted from the TIE Fighters.
The Rebel base was able to detect signals of the main squadron of TIE Fighter's but for some reason does not detect <PERSON>'s squadron of his TIE Advanced x1 and two TIE Fighters. 963