I have heard that there is some wood that should not be used in a cutting board because it can be 'bad'. I am not sure what wood is not good, but I guess some wood is poisonous and stuff. I use woods like pine, black walnut, cherry, oak, red oak, cedar, maple, hickory, and sometimes aspen. Are any of these bad? And if they are why are they? What should I look out for when making a new cutting board? Thanks!
To a great extent this is just the flipside of the question "What woods are good to use in a cutting board?" and there was a recent thread on this subject that was closed for being more likely to attract opinion-based responses. But you have asked one key follow-on question that doesn't come down just to a matter of opinion.
Are any of these bad? And if they are why are they?
As per the above it depends on who you ask, so this becomes largely a matter of opinion rather than there being some definitive yes/no checklist you can refer to showing what species should and shouldn't be used.
The example of western red cedar helpfully provided by Adam Zuckerman already is a perfect illustration of this, as not only is this species used for boards it's sometimes specifically chosen for use with food for the very chemicals it contains that make it an irritant (Google "planked salmon" for more). Some of the aromatic hardwoods chosen for burning when smoking food are also good illustrations of the same principle, because someone out there is likely to hold the opinion that "they shouldn't be used for boards because they'll taint the food" or something along those lines.
In terms of outright toxicity, not something like irritant/potential irritant properties, there are no woods you might buy and would consider using in a board that qualify, so you can put that worry out of your mind.
The thing you should focus on here as the woodworker is the risk to you when making the board, not any danger for the user from the completed board in any normal way. So while a given species might be perfectly fine in a board, you might want to avoid using it rather than risk exposure to its dust when sawing, routing or sanding it.
What should I look out for when making a new cutting board?
This is the only part where I think you can get input that isn't merely an opinion, because it's about wood's physical properties. And the primary bit of advice is not to combine species of widely different properties in a cutting board, for durability reasons.
Probably the main thing to focus on is avoiding combinations of species which have markedly different coefficients of movement (see table at the bottom of this previous Answer). This is for structural stability, because where pieces that expand more are locked between pieces that expand less it could put great strain on your glue joints and eventually split the board. Note: it doesn't matter if the glue is completely waterproof or how strong the glue joints are, because if necessary the board will split the wood itself apart to relieve internal stresses.
The other thing to bear in mind is using woods with very different hardnesses, if you're concerned with how the surface will retain its looks. So for example pine can make a perfectly acceptable wood choice for a board but it shouldn't be combined with something like hard maple because the pine will wear far more than the maple over time, leading to an ugly mismatch of surface textures.
Cedar (which has 12 varieties listed on their site at the time of this post) can cause both skin and respiratory issues. Several wood varieties can cause death.
Species: Cedar, Western Red
Reaction: irritant, sensitizer, runny nose, asthma, nervous system effects, NPC (rare)
Areas Affected: skin, eyes, and respiratory
Potency: 5 (out of 5)
Obviously you don’t want to use any softwoods, regardless of their grain density. They will show knife marks more than a hardwood in most cases. And, even though poplar is technically a hardwood, you’ll want to avoid it as it has very similar properties to pine. It’s just too soft and light to handle chopping and cutting.
Secondly, don’t use any species with open grain patterns; or, low grain density. Oak is an example of an open grain wood.Oak has very open pores which would attract bacteria, oils, etc..
The go-to/can’t-go-wrong woods in the US for cutting boards are hard maple and black walnut. They’re accessible, dense, closed-grain, and quite attractive as well.
If you want to use some exotics, some good cutting board woods are sapele and jatoba. Purpleheart is popular but can be very tough on your blades and tools.
Some “in-the-middle” species you’re probably familiar with are ash and hickory.
The woods that are most safe to use for cutting boards are those that bear fruits, nuts, or other edibles and have tight grain - Walnut, Cherry, Maple, etc.... A mix of walnut and maple make great cutting boards whether you're planning on gluing face, edge, or end grain. Also, make sure your glue is food-safe; I use Titebond III