While deductive inference is exposed to less number of and less serious criticisms, induction is exposed not only to more serious criticisms, but also is attacked on more than one ground.
Mill contends that syllogism is guilty of repeating the premises in the conclusion without moving further. This criticism applies to inference within the limits of classical logic, where only true premises are considered or where the premises are taken to be true. When such premises and conclusion are conjoined, we get what is called compound statement and such statement is called tautology, because the same thing is said twice. The aim of logic is to achieve progress in knowledge. Deductive logic fails to achieve this particular aim.
In the case of induction, induction is not regarded as logic at all since the truth of the conclusion does not follow necessarily from the truth of premises. Promptly, this objection was met by the defenders of induction by arguing that deductive standard ought not to be applied to inductive logic, lest the distinction itself becomes superfluous. As an alternative measure, some inductivists proposed what are called self-supporting inductive arguments. But any attempt to support one inductive argument with any inductive principle, if there is one, will, surely, lead to arguing in circle. This is so called because in this type of argument we are assuming what has to be proved which is a fallacy.
For quite some time it was believed that science follows a certain type of method which starts with observation of facts and ends up with generalization in the guise of law. This was the view of Bacon. Popper targeted induction precisely for this reason. While self-supporting inductive arguments involve arguing in a circle, any other attempt to justify induction results in infinite regress, i.e., if we use one principle to justify law in science, then this principle stands in need of justification, and so on. This is what is known as infinite regress.