Those under 18

Plans to live in a home for less than 5 years in a typical market

Going through marital conflict, especially a divorce that isn't finalized yet & where provisions haven't been established yet in a separation agreement to factor in real estate purchases.

Those who are unmarried & romantically involved who are considering cohabitation, where if a breakup were to occur, neither party could afford the mortgage.

Going through bankruptcy that isn't finalized yet.

High depreciation projection for the coming year, especially when combined with a projected decrease in mortgage rates.
 
Moving from 1 industry to at least one other in the past 2 years with some exceptions as described under "When to Buy"
 
Desire for increased flexibility in transitioning from one home to another with no desire to have an option to make profits during transitions
 
Job that forces one to rapidly move from place to place with no assistance for buying or selling from the job, or high job uncertainty with limited options for your profession in the area you're considering. For instance, a new principal at a school I knew well wisely lived in a hotel initially after moving from another state while many encouraged him to purchase, only to find that he lost his job within his 1st year there prior to moving back to his previous state. 
 
Free or significantly discounted rent available with family or others and desire to not rent out rooms to pay for the entirety of a mortgage or enough of a mortgage to cover everything but annual equity gains depending on the situation. One exception is if the same amount or a similar amount that you were getting for rent is available for a purchase, such as the Housing Choice Voucher program, also known as Section 8, being available to used for a purchase.

Seeking to move to a completely new area from another distant location (i.e. another state) not due to job or education, but because you think that life will be better in VA than it is where you are now despite never having lived here to try it out first.

Taking a job on in a completely new area from another state where you're currently based when you aren't confident that you'll have job security at that job for at least 3 years (i.e. a brand new job type for you, a job with no long term contract, or a brand new company to work for), especially if that employer has the only similar jobs in that new area. This case is particularly true of immigrants considering housing options who aren't moving to a location with family support geographically present in that new area.

Those in assisted living or hospice facilities, especially who have bought into them (i.e. for $300k) & who don't need to protect other assets to receive certain benefits.

Those with debilitating disabilities to the point where they are under the care of a guardian who is not advising a purchase or their (especially if a CPA is also consulted) or counselors are advising against a home purchase (especially if those advisors are owners themselves & not receiving compensation for the one with the disability to rent from them).

Those with a rapidly growing family, i.e. newlyweds who don't believe in birth control, who could end up with a "full quiver" of kids, & who either wouldn't want any kids sharing the same rooms or who would have difficulty abiding by law such as in VA no children over 2 sharing beds or sharing rooms with adults in most cases, no children under 7 using the top bunk of bunk beds, no children of the opposite sex shall share the same room during sleeping, as well as rooms having adequate sq ft for multiple children in 1 room (70 sq ft minimum for 1, 50 sq ft per child w/ 2+), & additional requirements as of 3/25/23

Low credit negatively influences both renting and purchasing substantially, but in each case, there are some substantial options for workarounds. Those with low credit are able to still rent some homes, and those with low credit or no credit are able to still acquire mortgages to purchase homes through the right channels and as long as certain conditions are met. However, low credit also can mean higher debts, so living in a worse home temporarily for rent while paying off high-interest debts more quickly before purchasing a better home can in some cases be beneficial as long as appreciation doesn't outpace, interest rates don't go up for the house, etc.

Unconventional Options - Neither Purchasing a Traditional House Nor Renting One:
Those actively engaged in or pursuing live-aboarding on a boat or similarly living highly frugally for their home environment (i.e. for <$200/month as my friends did at a dock in Yorktown (video link above) including utilities; see liveaboard column for local docking options here).