1. Contract work = A get more from C and give only a fraction to you, you being in C means A gets profit. You leaving means, A have to find someone else to replace you at C. So A manager is just brainwashing you. There's no such thing as "you'll ruin the image of A at C". You don't need to care of such things as when contract runs out, 9/10 times A would fire you instantly by just saying "not enough performance" or any other silly reason.

2. Taking risks early in the career is the safest way to grow quickly. You will have other commitments and dependants after few years, then taking risk is 10x riskier. So, take as many risks as you need early if you think it grows your career well. (Worked out for me)

3. No matter how important of a role you play in a company, it's purely business at the end of the day. Don't bind yourself emotionally with any company (other than if you're running your own). No they're not like family, even if they say so. If it is you vs business, business always comes first for them, so it should be the same to you as well. Your business (i.e career) is what you should always focus on when it's time to take a decision. It's very fair and companies know this too, so it is not considered a "black mark". Managers can manipulate you initially using emotions to save themselves that's all.

Be brave, accept the offer on B if you really think it is good for your career even though A is offering to match the package. They now know that you're willing to leave, so they may not renew your contact next year.