I'm 40 and I have never been married and do not have children. Nearly every woman I meet asks me "what's wrong with you?". Since we live in a feminized society that promotes marriage (the coffin) and children (the nails) as the norm, anyone who lives outside of that norm must have "something wrong with them". Everyone is so brainwashed into believing that monogamy and marriage is the righteous objective, that they never stop to consider the mountain of evidence proving the inefficacy of those institutions.
It's interesting because women never seem to consider the option that I am intentionally single and never married. It has always been easy to convince them that I am simply "picky" and have high standards because of my high value. It gets their imaginations churning on whether they will be the one I finally "pick". You always want the implication running with her that there are multiple women competing to get you. Women have wild imaginations and they are solipsistic, so they will naturally believe that other women want you if they themselves do. If you believe in your own mind that you are single by choice due to an abundance of women in your life instead of a scarcity, it won't be difficult convincing women that being single is a non-issue. By non-issue, I mean that your status of being single has nothing to do with an inability to attract women, and everything to do with you being a high status male with discriminating taste and high standards. However, if you believe that you are single because of some deficiency in yourself, they will pick up on that and likely perceive you as being generally undesirable by women, which will eliminate any attraction they have for you.
In other words, any stigmas that exist for single men over 35 have never created a shred of an obstacle for me. Always take any perceived weaknesses or "stigmas" and spin them as strengths. If a "stigma" is creating a problem for a man over 35, he should just do what women over 35 do: Get yourself a group of friends your same age and act like you're much higher value than you really are. Most men fall for this and it works wonders for post-wall women with sagging bodies and another man's children in tow.