Although this is a fairly basic question, I realized three very active users here put our answers in comments. Let me summarize:
1) It is risky to poke holes in any artery, let alone the aorta. Arteries are full of blood under high pressure. When you poke a hole in one, there is always some risk of serious bleeding. You also have to push against the arterial pulsatile pressure, making it more difficult to administer slow drips of drugs, as is often done with I.V. administration: either you are going to get high flow during diastole with high pressure, or you are going to get backflow of blood into the catheter during systole, or both. On the venous side, there is a lot more collateral circulation, too, so in an emergency you can usually close most veins without severe effects. Some drugs can be toxic to the local vascular environment, as well, which is again safer in a vein should it occur. Note that for some special procedures, such as angioplasty/stenting, arterial access is necessary, but this isn't true for drugs. (Thanks @Chris and @anongoodnurse)
And the aorta? Depending on body fat and where on the aorta you want to target, you are talking about a needle inches long, poking into a vessel you can't see, after passing other organs and tissues, versus veins, some of which are specially located near the surface.
2) IV drugs aren't "delivered" specifically to particular targets in the first pass: they dissolve in the blood, flow around the circulation, diffuse in and out of tissues, and eventually partition according to their binding affinity, hydrophobicity, etc. Therefore, drugs are going to go through the liver anyways. In fact, many drugs are metabolized by the liver, and some aren't even delivered in their final active form: metabolism may be required for activity, and often the liver is involved. Essentially, if a molecule isn't stable enough to make a pass through the liver, it won't be a useful drug or needs to be given in a higher dose to account for the high rate of metabolism. (thanks @Chris and @anongoodnurse)
3) Further, most IV drugs are given through easily accessed veins such as in the arm: these return to the heart before any pass through the liver or spleen. Unless you were trying to deliver the drug to the arterial circulation of that particular hand, it's going to circulate before it gets to the target organs. And if your drug is going to damage the liver, why don't you think it's going to be dangerous for anything else?