Most "poor" countries to which we send aid, are being plundered just as hard, or even harder. Every time we send food aid to some poor African or central American country, the local farmers get no money for the little food they produce and the local market is ruined, stopping local production of food instead of encouraging it.
You are right, except it's not the West that causes it. In most cases it is the government (both state and local) that causes economies to get worse even as aid increases. In many cases these governments are corrupt to some degree, so the aid intended for local farmers or communities never gets there. The aid tends to go either to the military (purchasing soldiers is a lot more expensive than one would think, and it pays to keep soldiers happy-notice how many undemocratically elected third world rulers have military ranks?) or in the case of a tame military to personal residences and bank accounts.
In political science there is a theory that is known as the resource curse, whereby a state that has an abundance of a natural resource finds its growth hampered by that resource, so that it is poorer than one would expect. This is caused by a number of problems, such as a failure to diversify the economy or internal conflict (ie, war) over the revenue. However, a major cause of this is government corruption and revenue mismanagement. The government either diverts the proceeds to their own pockets or, expecting the revenue to continue at high levels, fails to invest the money back into the economy and spends it on pet projects to remain in power.
Now, this is kind of perverse, but think of poor people as a natural resource. As long as the people remain poor, the aid continues to come in. If the aid continues to come in, the local political elites are able to allocate that aid in ways that continues to enrich themselves while allowing them to remain in power (paying off cronies/the military/subsidies). If they invest the aid properly, then the economy grows, the poor get less poor, and as they get less poor they have more energy and resources to invest in things such as politics, demanding a greater say in how they are governed. This demonstrates a direct threat to the ruling elites, who as a general rule are not strong leaders, as they rule by economic coercion or the threat or actual use of military force. So, essentially, in order for them to remain in power it is in their own self interest (not a fan of rationalism, but sometimes it just fits) to keep their population poor. In a nutshell, this is one big reason why Third World states tend to remain poor even when they receive large amounts of foreign aid.
Ideally, the aid given to these states should be neither financial nor edible. The investment should be in infrastructure (roads), and in raising the standard of living (water filters, solar panels/crank generators, farming equipment, etc). Investments such as this help the poor and are much harder to divert or misallocate (can't exactly wire a shipment of solar panels to a Swiss bank account). You are correct that these people are perfectly capable of helping themselves given the right tools. The problem is getting the tools into the hands of the people who need them, not those who want them.