Before you are hired and during your employment, your manager usually has to justify having you on staff. This is a very personal activity between you and your manager, involving investment of time and energy on their part. You also mention a "client" which means that you manager has also spent time "selling" you to the client. Justifying why you are the "right person for the job."
Perhaps without your knowledge, you have been under review, criticized or made mistakes that your manager spends time handling. This creates a human desire for some kind of demonstration of appreciation and/or loyalty in return, whether you realize it or want it.
Your lack of concern for the relationship is one way to lose it. If you are "keeping your options open" why should your manager invest any more time or energy in helping you advance your career? Why shouldn't he also keep his options open and advertise for and/or interview other candidates for you job? Just in case a better candidate comes along. Then he could just fire you and have someone better, right?
Also, the cost and time of "keeping your options open" is real. You have to spend time and energy updating your resume, reviewing potential employers, etc. All of this is time and energy you spend thinking about and focused on working somewhere else. The concept of that is likely to make any manager feel uncomfortable on some level. They want to not worry about replacing you, and get work done.
Similarly, if your employer were interviewing candidates for your job while you working, it would probably make you uncomfortable. It would probably give you the impression, true or not, that they are unhappy with your performance. Also, you would probably begin to worry when they might come across a better fit for the job and simply fire you, "services no longer needed" style.
You need to realize that employment is also a relationship. Your manager is investing time and energy into you. If you do not value your relationship, then you take steps to find another one. Your question makes it sound like you do not value it, so it would not be surprising if your manager began to take steps to find someone that does. Just keep that in mind when you "meet for drinks" to discuss the situation.
Your response: you probably cannot respond well without "constraining your options." You probably need to remove your resume from the website that you posted.
If you sincerely appreciate and value your job, you should start your conversation with your manager by saying those things. Also, express that you did not realize how important you were to him (which appears to be the case). You need to assure your boss that you want to continue to work for him right now and for the foreseeable future.
Also, then express that you would like to have a good career. That involves you looking beyond your current job/role in some manner. However, this creates a possible dilemma in that you are not sure how to explore outside options appropriately or when to know internal options are available. You need your manager's help in understanding his role with this larger goal. Maybe there are projects he can get you involved in, provide you additional training, give you more challenging work, etc. Unlike a marriage or dating, very rarely is a "job" expected to be a career.
Give him some time to respond. Consider this an opening to a much longer conversation (perhaps one that will last for several decades - even across different jobs and employers for both of you). If he seems genuinely interested in helping you as a person, then as his career progresses it might make it easier for your career to progress. You can provide each other professional references, etc. This is about relationship building.
However, the focus at the moment should be on the moment. His feelings are hurt and you need to "apologize." That means removing your resume and asking forgiveness, in a sense. Since you don't have an immediate need to find another job, this approach will help secure your current job, open you to options that you may not be aware of and gives you a chance to reinforce your relationship with your manager. Your action was not egregious, but it requires a sincere and serious response. This might actually give you a "new job" but perhaps not in the way you anticipated.