It's probably not the platform behavior messing up, it's coded pretty solidly. It's likely my clumsy fingers just mashing the jump key a split second too long.
Still, if you gave a little more clearance and a little more room to make small mistakes in the early levels, it would make the game much more approachable to more people. Slowing down the spike wall would be good as well, and you can make it gain speed every few levels or so.
Like I said before, just allow people time to get used to the game gradually. The first few levels should be challenging, but not necessarily "hard." Since you're an expert at your own game the first few levels might seem like really boring levels for babies, but that's just not the case. Expertise comes with practice. You can't practice if you can't get past the start.
Another thing that keeps game levels interesting, and will keep players engaged, is a good level flow. Take a look at how other games set up their difficulty within a level. The start is usually somewhat calm, then the action ramps up, then there's a truly difficult bit, then it calms back down again for a moment. It's like a wave. Easy bits followed by hard bits, repeated over and over until the level is done. If it's all hard all the time there is no chance to catch your breath, and people get frustrated more easily and are more likely to put your game down.
Of course there is always a niche for super-hard games that start off hard and stay that way. And if that's what you're looking to fill then that's cool too. Just keep in mind that not everyone enjoys maso-core games like that. It's just a matter of which audience you're trying to reach.