In composing this speech, some level of research is needed. I think that it might be good to open with some examples of how our world has been impacted through both invention and the pressing need for it. Perhaps, identifying the invention of computing programs in the mid to late 1970s with the work of Steve Wozniak and Bill Gates/ Paul Allen might be a good start, only to identify that something we now see as commonplace was an invention that responded to the needs of the time and beyond. Another such example could be the standard Edison and the light bulb situation. If one really wanted to push the debate, Oppenheimer and the Manhattan Project "invented" the atomic bomb out of the necessity to defeat Hitler and the forces of fascism across the world. I think that developing the historical frame of reference that explains why particular inventions came about would be powerfully important. At the same time, I think that it is essential that the speech "hit" on the idea that human beings confront situations that allow them to posit new and divergent approaches to solving such problems. In this manner, it becomes elemental to understand that necessity is the mother of invention.
Throughout history, man has invented things as his need for them arose, and according to his understanding at the time. As a general rule, most men and women go along in life quite content with the way things are around them, until a situation comes along that provides a stumbling block (so to speak) to their forward progress. For example, a large rock rolls down the mountain and onto the road, blocking the highway and making everyone have to detour around it. The masses come and go until, invariably, someone eventually comes along who looks at the rock in his way, wants to remove it, figures out how to do it with tools and dynamite, blasts it away, then restores the road to its original condition and goes merrily on his way. Such is and always has been man's great ability to adapt, invent, and improve. This, I think, is the message behind the saying, "Necessity is the Mother of invention."
To be able to write a good speech on this subject you need to be clear about the meaning and significance of the statement "necessity is the mother of invention". It refers to the fact that people are likely to make any efforts to invent something new only when they are satisfied in some way, with what is existing and feel the need or desire for something different, some thing better.
Once you are clear about the significance of the statement, you can start looking for examples that support the statement. In selecting the example you need to look for cases where the link between the felt need or necessity and efforts made to invent means of meeting those needs is clear. You can also cite general cases like initial development of the entire field of chemistry or alchemy, as it was originally called was the result of people making the efforts to satisfy their desire for more gold. This case of origin of chemistry also covers another aspect of origin of inventions - though the thing invented may not be exactly what one was looking for in the first place, still that other invention would not have been possible without the efforts motivated by necessity.
Another point which may help you to counter the arguments of people opposing the proposition is related to the question of what is really necessary and what is not necessary. Here your argument should be that whatever is felt to be necessary by the inventor, is enough to motivate him or her. The fact that it may not be considered by some others is irrelevant to the motivation of inventor.