But I do have a couple of questions. First, about your premise that inductive reasoning proves nothing. Why? How do you prove that you even exist if not by inductive reasoning?
Every proof relies on
axioms. Axioms are those things which are accepted as true without proof. Descartes believed in only one axiom: I Think therefore I Am. He went on from there with various proofs of God's existence, the most commonly known being that he (Descartes) could not think of anything outside himself unless something was outside himself. Therefore, God (the cause) existed to (effect) make him think of God.
A question here to be asked is: What if your axiom is wrong? If axioms are wrong (and none are proven) then every proof based on that axiom is invalid. So how can you
know anything?
To this end we have developed various systems to determine what is true and what is false. Philosophy deals with these questions, and should not be thought of as separate from the scientific method. The scientific method can determine, with relative confidence, things that are probably true. The scientific method can prove that there are things that are untrue. One example is the Spontaneous Generation of Life - see Pasteur.
As one studies philosophy, you eventually encounter what is probably the most ground shaking proof in the history of mathematics and/or philosophy:
Gödel's Incompleteness Theorem.
"All logical systems of any complexity are, by definition, incomplete; each of them contains, at any given time, more true statements than it can possibly prove according to its own defining set of rules." This infers that "
rational thought can never penetrate to the final ultimate truth. "
As one comprehends Gödel, some give up asking how can we know anything. Others go forward with relief, realizing that there is truth outside of the provable/logical. The latter is actually very liberating. Now, ask yourself the following. Do we just forget that truth, moving on as if it does not exist, or do we try to find that truth? In addition, if you look for it, how do you figure out what is true and what is false.
The study of how we know something is epistemology. We all base what we know on four basic sources:
INTUITIVE KNOWLEDGE takes forms such as belief, faith, intuition, etc. It is based on feelings rather than hard, cold "facts."
AUTHORITATIVE KNOWLEDGE is based on information received from people, books, a supreme being, etc. Its strength depends on the strength of these sources.
LOGICAL KNOWLEDGE is arrived at by reasoning from "point A" (which is generally accepted) to "point B" (the new knowledge).
EMPIRICAL KNOWLEDGE is based on demonstrable, objective facts (which are determined through observation and/or experimentation).
The question now becomes one of order and importance of the above sources of knowledge. To declare that you will only use one, or two of these is to declare that you
choose to ignore some truth. Some people choose to mock one or two of the above, but to do so is to mock truth, and demonstrates another
choice to limit knowledge of the truth.
Now, back to you question. Inductive reasoning is a good tool. I hope that you can now see that by itself it is woefully inadequate to prove anything. Evolutionary theory is an example of inductive reasoning because it is one scenario that fits available evidence. In other words, it is a guess, even if an educated guess. Many of the scenarios from the Intelligent Design crowd also fit all the available evidence, but certainly begs the question as to the identity if the designer. Inductive reasoning can point you in the right direction, but can never bring closure.
Deductive reasoning, on the other hand, is the foundation of Mathematical Logic and any conclusion drawn is just as valid as the axioms on which it is based. To disagree with a conclusion based on Deductive reasoning is to disagree with the axiom. To disagree with a conclusion based on inductive reasoning is simply to provide another scenario that fits the evidence.
Secondly, I don't think the fault lies with "Modern Education" for not thinking critically, but with people who are unwilling to think critically. It takes effort. People don't want to do that.
I might be wrong. This is certainly based in inductive reasoning.

I believe that if more people are taught critical thinking, then more people will think critically. The problem moves beyond secondary education, but does seem worse there. In college, most people train for a profession rather than seeking an education. Therefore, we produce adults able to make a good wage, but who have not learned valuable thinking skills.
Note: All the above is taught in any good Intro to ethics/logic/philosophy class. These things should be foundational, taught to everyone in High School. Most of us, however, never study ethics, logic, or philosophy. I did not learn most of these things until I went to grad school in my mid-30's. I was introduced to Gödel here on Anandtech.