Because an invasion is a huge deal. To be a bit crass, it's not like Civilization or Europa Univeralis or something where you drop some "army" unit onto the enemy territory and then you just rampage. I have little doubt in my mind that the Germans could have, if they so wished, snuck at least a token invasion force onto British soil. They could have slipped by and landed maybe even a significant landing force and done some real damage. The issue comes with, then what? Take D-Day for example -- the men who took the beaches didn't just take over France all by themselves. They needed reinforcements. They needed supplies. They needed all sorts of things to keep the offensive moving. Perhaps Germany could have rushed across in the chaos of the fighting, but the fact is, once they established a beach front, the British would just decimate them and cut them off.
The fact is, at every single point of the Battle of Britain, the British severely outnumbered the Germans in air power. Between June and October 1940, they had, on average, a ~340 plane differential. During the height of the fighting in August, the British would lose 204 aircraft but build 476 more. In the same span, the Germans would lose 397 but only replaced 313. The number dead was even more appalling -- the British noting 104 pilots killed in the fortnight and the Luftwaffe noting 623 dead or captured.
So the reality is, the Germans couldn't even maintain aerial dominance or even some level of control. They were never even winning the aerial battle itself. Without a navy, and without aerial dominance, how does an invasion force even begin to think of acting in any long term manner?
Max Hastings Inferno gives a wonderful account of the Battle of Britain, which is where I've gotten my numbers.
Because even if the Royal Air Force wasn't able to intervene in the landings, the Royal Navy surely would be. The Normandy landings were difficult enough with total, uncontested, absolutely unbreakable naval superiority. Even a single destroyer could wreck havoc on the German landing craft, without giving them a prayer of retaliating, and the Royal Navy had a lot more than a single destroyer. The Germans were relying on air superiority to give the Kriegsmarine an edge in securing the Channel. Without that, they could never contest the Royal Navy, not that it's likely that they could with it.
Besides, as /u/elos_ already stated, landing troops in Britain wasn't a surefire win. The Germans lacked assault craft comparable to the American ones available for D-Day, and couldn't even really transport their entire army with the civilian fleet they were trying to scrounge up, so a contested landing would be tricky to deal with. This is compounded by their lack of specialized transports for armor or artillery, so their infantry would be landing alone and unsupported. No air superiority meant that they couldn't rely on air support to fill the artillery's gap, either, and and no artillery includes anti-aircraft artillery, leaving them even more vulnerable than normal to the enemy's air support as well. They didn't have access to the massive artificial ports that the Allies built for D-Day, so supporting the army would be a logistical nightmare that makes Barbarossa look decent by comparison, even if the Royal Navy politely stayed in its ports and didn't raid any of the supply ships. And, on top of this, the army that they would be facing would be the full might of the well trained, well prepared and highly motivated British Army, rather than the rear echelon troops faced by the Allies at D-Day. Whatever force they managed to land would not have lasted long even if it somehow managed to get off the beaches. Even if the Battle of Britain had ended in their favor, a successful Sealion operation is doubtful, perhaps impossible. Without success in the air, they had no chance.
In addition to the points /u/elos_ and /u/LiterallyBismarck have raised, a third difficulty is that Operation Sealion wasn't anything close to a workable invasion plan. Nazi planning had been premised on a British surrender following the fall of France, and it was only when this didn't eventuate by early July that invasion plans began to be drawn up. The result was Sealion, a dubious set of goals based around extremely optimistic assessments of available German resources and British capabilities. This plan had the support of an over-enthusiastic Heer (in one of the first drafts the invasion was described as a 'river crossing on a broad front') and no one else in the German military leadership. The Kriegsmarine considered it sheer madness while the Luftwaffe believed it was unnecessary as they felt war could be won from the air. It was also a complete rush job: Hitler's July 16 directive gave the OKW until mid-August to prepare the invasion (preparations included the disabling of the Royal Air Force).
Not only that, but at the highest level, Hitler never evinced any belief in Sealion. By July 1940 he was already switching his focus to the Soviet Union and gave little consideration to those who wanted Germany to focus on defeating Britain first. The German armed forces were not equipped for a big, extensive series of naval/land operations and to Hitler's thinking Germany couldn't afford to dig in for a prolonged siege of one of the world's greatest naval powers. Invasion could be a useful diplomatic bluff, and Hitler kept the option open until deep into September 1940, but all indications are that he considered it a last resort.
The Battle of Britain was the German answer to the dilemma of what to do about Britain. Goering promised Hitler that the Luftwaffe would destroy the Royal Air Force, and this would either bring British surrender itself, or make invasion possible. The Nazis were never completely clear which of these was going to eventuate. The feeling among the Luftwaffe was that airpower could achieve victory on its own, and that decisive air supremacy could be accomplished quickly. Both turned out to be illusions, but these were the founding illusions of Sealion: incredible success on the high seas was predicated on incredible sucess on the air.
Sources:
Stephen Bungay, The Most Dangerous Enemy: A History of the Battle of Britain
Ian Kershaw, Fateful Choices: Ten Decisions that Changed the World, 1940-1941
Thank you /u/elos_ , /u/LiterallyBismarck , and /u/chairs_missing for the explanations and valuable info! I guess for whatever reason it had never occurred to me that the fact that the Kriegsmarine was much smaller than the Royal Navy would be a hindrance to landing operations, but in hindsight it makes absolute sense. That said though, I'm curious as to why, perhaps, a larger effort wasn't put into winning the air war; surely the Germans would have been able to concentrate the might of their industrial capabilities to eventually outmatch the British output (unless of course American shipments came in)? Was Hitler simply that determined to invade the Soviet Union and start the second front that would ultimately bring his regime down?