The first contradiction is that innovation requires a business to embrace processes and methods that are far different from the efficient, effective processes that sustain short term profitability. Innovation creates new, risky, uncertain concepts that will pay off in quarters if not years. Most "business as usual" processes reject these kind of ideas as contradictory to the existing operating model. Which is like eating your seed corn. I addressed this issue in my book Relentless Innovation.
The second contradiction is that while executives want innovation, they don't want the disruption or investment that innovation requires. This simultaneous demand for innovation results and refusal to invest in innovation efforts creates dissonance in the teams that are actively trying to do interesting innovation work, and leads to confusion and then cynicism.
The third contradiction focuses on the importance of transparency, visibility and commitment. Most innovation activities are isolated in the far reaches of a business, far from prying eyes and easily swept under the rug if the innovation doesn't pan out. In an era of vocal leaders, we need far more emphasis on innovation, rather than the circumspect way many organizations approach innovation, out of sight and out of mind. Doing innovation work is tough, and doing it without the full support of the senior team, constantly demonstrated, means that many innovators have far fewer resources than they need.
The fourth contradiction, and perhaps the biggest barrier to innovation, is the contradiction between what we TELL people to do and what we PAY people to do. Often we express the importance of innovation and assign people to innovation teams. We ask them to do important work, creating new products or services. Yet we do nothing to change how these individuals are evaluated, compensated and rewarded. In fact most of these people are held accountable in their evaluation period to the work they did in their "day job". Which leaves the potential innovator in an awkward position - follow his or her passion and spend time on innovation that may detract from success in the day job, or work on the day job and give short shrift to innovation.
There are more contradictions than these I've listed. I hope you'll be willing to add your own in the comments section. Perhaps my other favorite is the old saw about protecting interesting ideas from others, to keep them from stealing your ideas. If an idea is truly unique and disruptive, you won't have to worry about anyone stealing it - you'll have to cram it down their throat to get them to pay attention. Oh, the irony of it all. Perhaps it can best be said that good innovators are people who recognize the irony in their work.