When he tries to fix the problem and your just trying to vent ask him to let you finish talking first, explain you want him to just listen as you were stressed throughout the day and just need him to be a pair of ears at the moment. If after your done he has solutions listen to his response, even if its not a good one just thank him for listening and you apprechiate him.

For him not wanting to talk about his feelings and emotions their isnt much you can do about that outside of reassuring him your their if he ever wants to talk and making sure he is comfortable doing so.

On option for councilling is for you to start out solo and then try and have him join in after you have gone a few times, this way he may be more willing knowing you have gone and you havent left him. Try explaining its not about fixing but its about growing together and becoming better for eachother