Can recycling be bad? It depends on what is being recycled.
Some recycling is bad: in these cases, the cost (in money and/or the environment) is higher than what it saved. Some recycling is good: the cost to recycling is less than what is saved, or in some cases minimal.
Paper recycling, for example, is mostly good. Though it can also be bad, depending on what the plant does with the shreds: instead of providing wood pulp to a paper mill, you provide it with paper pulp: basically the same thing, except you didn't need newly cut trees. There might be a slight environmental cost associated with the process since recycled paper still needs to go through the same bleaching process as virgin pulp. Unless the paper mill is set up to sort through the trash, separate out the paper and shred it the transportation costs and impact make recycling it a loser. It is almost always cheaper and less environmentally costly to truck trees from the forest right to the mill rather than collect paper, truck it to a sorting facility, sort and shred, and then truck it to the paper mill. This assumes the trees are coming from sustainable tree farms, which is usually the case.
Plastics, however, aren't always so good. Some plastics need a lot of chemicals to get them into a state you can use them again; and in some cases, the chemicals required to recycle or the byproducts of recycling them are worse than the costs associated with making new plastic.
This happens when breaking down the plastic into monomers is either a very dirty process or chemically impossible if the polymer has been cross-linked. You can just grind it up and use it as filler, but the applications for that are limited. In the end it usually requires more energy to recycle it than to make it from crude, especially when you factor in transportation.
You'd have to do specific research into any given recycling program to know where on the "good-bad" spectrum any given recycling program is.
Metals are almost always worth recycling.
Aluminum is the absolute best thing to recycle, since it only takes 5% of the energy to recycle a can into a new can versus making a can out of bauxite.
The refining and mining has already been done, just need to melt it and recast. It is both cheaper and more environmentally friendly than making more metal from virgin material.