There are many issues with this debate.
Primarily, scientific terms have specific definitions UNLIKE words in everyday speech. When we say scientific theory we are using the scientific definition of theory.
Theory: an explanation, based on direct and extensive observation that has been tested, rigorously, and has been verified as being accurate.
So it means nothing to say that teaching Evolution is different from teaching the theory of Evolution, they are one and the same.
Additionally, Intelligent design is not a scientific theory by nature of it's arguments. It supposes that supernatural events lead to the existence of all or most of the creatures on earth. This alone rules it out of the realm of science because science is the study of naturalistic cause and effect scenarios. We observe a phenomenon and examine nature in an attempt to discover the cause of the phenomenon. This is not a new development, the rules were not amended to exclude supernatural causes when Intelligent Design was anounced. It has been like this since the Greeks, and it continued up through the Renaissance to modern times.
Intelligent Design is metaphysical science while Evolution is naturalistic science. They are inherently non-interchangeable.
Irreducibly complex: the idea that no part of a biological organ or organism can be taken away or reduced in complexity and still produce a working part or organism
This is fundamentally incorrect as it supposes a purpose for the given organ or organism. The human eye is often used as an example. The claim is that the human eye is no longer a functioning human eye if you remove a piece of it. And in making that statement they have named the function of the eye so that anything less is in fact no longer an eye. But in reality there are sundry forms of less (and more) complicated eyes in the natural world and just because we know what ours are capable of does not mean that they'd be useless if they were less complicated than they are currently. A photo receptor (light sensor) is better than complete blindness, fuzzy vision is better still, the human eye is yet one step up, and an eagles eyes are one better. Irreducible complexity is hand waving at best.
And, probably most importantly, Evolution does not claim to explain the existence of the universe, it explains how natural processes lead to ever more complex biological entities. DNA was not formed by lightning striking a primordial soup, that may be a nice cinematographical image, but it is not a realistic explanation. In reality, chemicals bond with one another, everything we see around us is composed of chemical elements bound to other chemical elements. Nucleotide bases are no different, they are just bound collections of hydrogen, oxygen, carbon and nitrogen. DNA is a chain of nucleotide bases that have, again, bonded in a stable manner, no lightning needed, no designer required, it happens as naturally as water (hydrogen bound to oxygen, though admittedly less abundantly and in a more complex way, but even water is scarce through out the universe). From there, chains of DNA are still more stable, and at some point we have life.
Maybe a supernatural being stepped in somewhere, and maybe not. The point is that science is the study of nature, and therefore requires naturalistic answers to the questions we pose. There are places for both Evolution and Intelligent Design, but they are separate places and can never be united until someone finds a way to examine the Designer in a naturalistic way.
Sorry for the ramble but I have family members that work in the field of Evolutionary Biology and it is, obviously, frustrating to have so many people misunderstand something that is essentially irrefutable. this is not intended to be an insult, it is just the state of affairs currently. The fact of the matter is that you'd have an easier time disproving the notion that an object has mass than you would trying to refute evolution. Mass (the entity that gives everything in the universe weight through interaction with gravitational fields) is, as of yet, undefined in a proven scientific theory, CERN's Large Hadron Collider should straighten things out, but that's another year away. Let's all cross our fingers and cheer on Mr. Higgs.
I.D. is like one guy saying to another that he uses a straight razor to shave his face and the second guy replying that he does too, then proceeding to take out a cardboard cutout of a straight razor, lather up with Cool-Whip, strop the cardboard on a scarf, and rub the cool whip off of his face, it's just not the same. To some, it looks about right, but upon closer inspection it is anything but.