Over the last four years I have watched this cycle repeat and think I've found a formula for a successful transition from Cub Scouts to Boy Scouts. I used this tactic with my sons and it worked. Unfortunately some families who do not do this wind up confused or misunderstanding Boy Scouting or have sub-par or negative experiences, then quit. So, I suggest you give my method a try.
First, pick a Troop carefully. If you can camp with them first, you will learn a lot. As BSA requires a parent must camp with a Webelos Scout so while the parent is there I advise that the parent both observe what goes on and also use that time to discuss the Troop with other parents and the leadership.
Before I tell you my plan, I want to urge you that if your son does not like the Troop you have chosen, after making a serious effort (which I will describe below) before quitting Scouting please try another Troop. If he did like Scouting but just isn't clicking with this Troop, find another to try. Doing that also teaches the boy to not give up and quit but to work toward what they want which sometimes means trying plan B. Each Troop is a little different so finding a right fit sometimes takes two tries.
First, upon crossing over from Webelos in the spring, attend every single Troop meeting until summer break. Your son will get to know the other kids. Sure, not every other Scout may attend every meeting but your goal is for your son to get to know those established Scouts. By not missing meetings your son will not be out of the loop with communication either.
Second, the parent should stay at the meeting if possible, not to spy or to babysit your son, but to talk to the leadership and other parents. Ask questions about Boy Scout program. You, the parent, need to understand the process of rank advancement and the processes and procedures that the Troop uses. Even within the structure of BSA there is wiggle room as to how the Troop operates. If you understand the hoops that need to be jumped through you can explain them to your son so he can achieve success in his Scouting experience. As an adult your may find the policies and procedures complicated to learn all at once, so imagine your ten or eleven year old son's possible confusion.
Sometimes a boy is overwhelmed at the activity at a meeting and he may miss important announcements such as what fee to bring to the next meeting for the campout food charge or if a permission slip is due on a certain date or that a camping trip is happening in two weeks. They may miss a sign up for a camping trip or some other activity if they don't hear the information as they are distracted or not listening. Boys who are ten and eleven years old sometimes miss details like that which are important if he is to fully participate in the program.
Your son should attend every camping trip that first spring. There are many reasons to do this. First, your son will be able to bond and make friends in the Troop. A lot of bonding goes on at camping trips that don't happen at Troop meetings. Also, Troops sometimes do special activities at spring camping trips to help the brand new Scouts learn mandatory Scout skills required for rank advancement. If your son misses that window of opportunity they may have to either work hard in a privately arranged session to learn them or they may have to wait for fall. For example if they miss the opportunity to earn the special requirement to carry and use a knife or to make fire, it can negatively impact them for the next 3-6 months when the next chance may be to earn those.
If your Troop does a summer residence camp, they should attend. Your son will make friends and bond with the Scouts in the Troop in a week of summer camping far and above what happens in a weekend camping trip. Scouts also get to do more things than they often can do with the Troop such as kayaking, water trampoline swimming, rock wall climbing and shotgun shooting to name a few. Lots of good memories are sure to occur and horror stories of bad rainstorms or bad camp food or other such things will be things to laugh about later. They will learn more Scout skills required for rank advancement. They will earn their first merit badges. If your son is ten or eleven and has never slept away for a week this can be a safe and responsible opportunity. Remember they are not going away with strangers, they will be with leadership from your Troop that you will have gotten to know over the last three to five months.
In the fall continue to attend all the Troop meetings (or nearly all). In the fall new Scouts usually join a Troop. Now your son will feel like a veteran member of the Troop and the newer kids will (temporarily) feel like outsiders. Your son will feel confident and suddenly instead of being a newbie they are looked up to by the newcomers. This is confidence and self-esteem building. Your son can begin acting like a leader to these newer Scouts.
Fall campouts usually offer different opportunities than the spring camping trips did. More Scout skills will be learned. Any rank advancement Scout skills can usually be worked on if your son initiates it, and camping trips are sometimes perfect opportunities to practice skills and then to get signed off on completing them.
The first Court of Honor held in the fall will be ego boosting for your son as by now he will have at least earned the Scout rank if not also the Tenderfoot rank. If he went to summer camp he should have completed at least one merit badge.
At this point one or two months into the fall, your son should realize if he enjoys Scouting or if it is not for him. Having toughed it out by going through things such as rainy camping trips and eating burned food that he made, he will have built some character as well and will have some memories to laugh about with his fellow Scouts.
It may feel uncomfortable to join a new Troop not knowing anyone or knowing just a few people but it is a good social skill for kids to learn to tough this out and forge new friendships and acquaintences in the new Troop. He will get through it if you nudge him to attend regularly and to actively participate in the various activities. He may learn to love camping trips when he previously assumed he'd not like camping.
My suggestion is to Troop shop and pick a Troop that you think is a good fit that has good leadership and a good group of Scouts. Then dive in and fully participate.
I suggest active parenting not helicopter parenting. Let your son have independence and learn to advocate for himself as he navigates his way through the rank advancement process. It is one thing to help your son organize himself and to learn to listen to announcements for important details about activities and opportunities but it is another thing to do all his thinking for him. This is a time for a boy to start learning more independence and autonomy in a safe environment.
I wish your son(s) good luck with Boy Scouting. I hope they have as much fun as my own sons have been having.