Personally, I find blanket generalizations problematic. To say something about "every manager" presumes, logically, that not a single manager in the entire world is exempt from your claim. That is why one should avoid beginning statements with words like "every" unless one is talking about certain types of logical or scientific truths (e.g. "Every bachelor is an unmarried man" is true because "unmarried man" is the definition of "bachelor," or "Every object has mass" is inherent in our sense of what objects are).
On the other hand, I would agree with the statement that "human resource management is an important part of most managerial jobs." In general, as a manager, one manages people and to do one's job effectively involves choosing the right people for a given task and providing the sort of leadership that helps them succeed. This can involve fostering and nurturing talent by selecting people for enhanced training programs, identifying people who might be ready to take on increased responsibilities, mentoring people and providing guidance, and using various tools to incentivize performance. Essentially, your productivity as a manager means maximizing the effectiveness of the people you supervise.
I would not agree that every manager is a human resources (HR) manager and nothing else, but I would argue that HR management is a part of every manager’s job.
HR management can be defined as the process of recruiting, selecting, training, evaluating, and rewarding employees. Its goal, as the link below tells us, is to “maximize the productivity of an organization by optimizing the effectiveness of its employees.” When we keep this definition in mind, it should be clear that every manager’s job does involve acting as an HR manager.
Of course, not every manager is involved in recruiting and selecting employees. To this extent, it would not be right to call every manager an HR manager. However, the rest of the definition of HR management does apply to every manager.
For example, managers are clearly involved in training their employees. Once an employee is assigned to them, they will be training that employee on a daily basis, even if they do not formally do so. As they do this, they will evaluate the employees. It will be their evaluations that help to determine whether the employee will be retained or promoted. In general, each manager is clearly trying to improve the effectiveness of their employees by supervising them, correcting them, advising them and motivating them.