What’s wrong with this induction?

P1) Lots of animals lay eggs

P2) Animals are things

C1) Therefore, lots of things lay eggs

P3) People are things

C2) Therefore, lots of people lay eggs

I know that there’s something wrong with this inference but I can’t determine where.

Also, does anyone know an article that shows how to use induction properly and correctly?

I see at least 4 issues with the argument:

1) The expression "lots of" is undefined so we're left open to (a) different readers interpreting "lots" in different ways and (b) a reader or the proponent intentionally or accidentally using a different interpretation for "lots" in different statements.

• We could probably agree with: P1 All animals are things; P2 Some animals lay eggs; C1 Some things lay eggs.
• We'd probably have less agreement on whether the "some" in P2 and C1 constitutes "lots".
• As it is, we're left with the possibility of P1 being false, because of our understanding of "lots".

2) I see an element of the  fallacy of (the) undistributed middle in that the premises move from "lots of animals" to "things" to "people" to "lots of people".

• For the series P1/P2/C1, we have two classes of objects (animals and things) with animals being a subset of things.  Since we can all think of "things" that are not animals, the number of things has to be greater than the number of animals.  There's no evidence given about the number of non-animal things, whether or not any of them lay eggs, and whether the proportion of things laying eggs is sufficient to be considered "lots".
• As an example, let's assume there are a million animals, of which 1/4 lay eggs.  Even if we were to agree that 1/4 million out of 1 million actually constitutes "lots", 1/4 million might be only a "few" if we consider all other non-animal things.  Perhaps we could agree that there are 3 million non-animal things (chairs, rocks, trees, cars, snowflakes, highways, etc.) then, even if we think 1/4 constitutes "lots" we probably wouldn't think the 1/4 million of the total 4 million (i.e., 1/16) of all things would be "lots".  The best we could conclude is that "some things lay eggs".

3) The lack of clarity about the quantifiers creates problems.  This series of statements alternates between providing a quantifier ("lots of") and offering no quantifier at all (opening to the question of whether the statement applies to all, some, none, or ...).  The argument would become very different if we were to inject different quantifiers where none exist:

• Lots of animals lay eggs ... few animals are things ... 
• without having quantifiers in the original argument, we're left guessing what the proponent means.

4)  We also have a non sequitur in the latter (C1/P3/C2) part of the argument.  Even if we accept that "lots of things lay eggs", that statement (because it doesn't say "all things lay eggs") tells us that there are some things that don't lay eggs.  There is a missing link between things that lay eggs and people, leaving the possibility that people lay eggs no more likely or logical than the possibility that people just might be the sort of things that don't lay eggs.

This is a deductive argument, not inductive.  

C1) says "lots of things lay eggs."  It doesn't say "all things lay eggs."  So there's no reason to think that people (which per P3 are things), are among the things that lay eggs.  People may be things that don't lay eggs.

Again, this is not an inductive argument so it doesn't commit an informal fallacy.  It is a categorical argument (developed by Aristotle)-- and commits the fallacy of Categorical Logic called the Fallacy of Undistributed Middle.  It is a fallacy because neither C1 nor P3 makes an assertion about all "things".

It's equivocation.

Just because humans and animals are things, doesn't determine that they are the same thing in function, because the term, "thing" is not the attribute for this.