Why was my recent asthma attack at work not enough for my boss to give me sick leave, shouldn't it be?

Many issues. Employee law is a minefield of different problems that vary from state to state. Depending on the number of employees, status of employment, contract provisions within that workplace, etc. the employer may or may not ever need to offer any. If your contract doesn't specify sick days as a benefit, don't expect it.
Depends... Asthma is a controllable condition so, with treatment, you should be able to live a normal life, including working. If you think you need time out of work to recover, see your doctor so this can be assessed and an out of work note provided, if necessary. Your doctor can also get you back to work as quickly as possible by providing the proper therapy. Good luck!
Yes, but ... Your boss probably has either been burned by people overusing the excuse or is ignorant or how serious a problem asthma is.
Depends... If your asthma is not properly controlled, you need an adjustment to your meds, and that is done best without changing your daily routine. On the other hand, if your job contains a severe asthma trigger to which you are highly sensitive, either it needs to be removed, or you need another job.