Sit down child, it's time for a talk.
I've been supporting for around 6 years or so, and you see a lot in this role you really do. What's important though, is to make sure you're focusing on what you can do, how you can improve, and where your time is best placed.
ADCs are a varied bunch, some are really dumb, and some are absolute monsters, and you can't expect to get the latter every time you queue up. That said, some ADCs are dumb because they're overconfident, and some need guidance. Good communication with your carry can make the difference between a hellish lane phase, and something resembling actual teamwork. When you can, try and get on the same level as to where you and your carry want to be. If you don't feel confident in trading, let them know, If you think they're being too aggressive gently warn them that you either can't or won't match that aggression. Being honest, but sympathetic tends to be how I keep a lot of my carries out of trouble, and honestly I've found that I rarely get flamed. By and large I do feel that the vast majority of Marksmen I've played with over the years have been great people, with only the occasional bad apple.
Second, establish rapport. I can't stress this enough, supports often complain about not getting enough credit for doing good things, well sometimes you have to give to receive, and in this case, it can really help your carry if you compliment them on things they do right. Not only do a lot of people reciprocate the compliment, especially if the two of you are doing well, but I find it makes them trust you a bit more, because they know you're not just on their asses because you hate them. A little bit of trust can go a long way, and help lend that critical bit of validity to criticism you do give, and can help both of you be in a position to adjust to the other's needs. You don't have to kiss ass, just a simple acknowledgment of things they do right, generally kills, CS, etc.
Third, some Marksmen are just completely too far gone. Either they're tilted to the moon, or they're just not very good people to partner with. If a Marksman decides that they're going to spew nothing but ridicule, then make use of the mute button. An ally who is more likely to tilt you, is likely more detrimental to your play than any potential insights they might give later down the line. If they're assholes, but are doing well, continue to support them so long as its beneficial to the team. If they're tilting and they're really bad, come mid-game once you aren't bound by lanes, seek out the most impactful member of your team and attempt to help snowball their lead instead. Supporting the Marksmen is part of our job, but our overarching role has always been to "Keep the damage rolling". If the marksmen isn't the source of damage that needs protecting, you don't always need to go out of your way to save them, especially if you fed mid who is cooperating with you might be better served by your protection and CC. Just because you start with the carry doesn't always mean you have to stay with the carry, especially if they aren't....y'know...carrying?
Final tid-bit. Always remember that you aren't going to win every game. Ideally you win more than you lose, but remember that part of the whole experience is learning how to improve. If you're losing, that generally means there are things you can improve on. Just because we aren't the main damage dealers doesn't mean we have no agency as to how our games go. Sometimes it's about roaming and finding good places to help snowball more competent players. Sometimes it's about being able to talk a team of misfits into getting their acts together. We're a powerful asset to any team we're on, so we have as much say as anyone whether we win or lose. Focus on what you might be able to improve, and gradually as you get better, you'll find yourself being able to handle situations which seemed completely unwinnable to the you of the past.
Also Pick up Bard because he's great, no I'm not biased 