Q:

Why might mindfulness and meditation lead to anger and anxiety?

Background: I have been trying mindfulness/meditation but I don't understand how to do it. For example, I tried sitting thinking and focusing on my breath, but thoughts kept intruding, so I just observed them, without trying to suppress them. Soon, one thought led to another, I felt myself getting angrier and more depressed. By the end of my meditating session, i felt terrible, anxious and agitated. 
General Question:

Does meditation and mindfulness cause many people to get anxious and angry?
Why might meditation and mindfulness lead to anxiety and anger?
Is a positive response to meditation related more to the method or the person?

A:

I have found several studies which support the general consensus that mediation helps to ease anxiety.

Bahrke, M. S., & Morgan, W. P. (1978). Anxiety reduction following exercise and meditation. Cognitive therapy and research, 2(4), 323-333.
Krisanaprakornkit, T., Sriraj, W., Piyavhatkul, N., & Laopaiboon, M. (2006). Meditation therapy for anxiety disorders. The Cochrane Library.
Tacón, A. M., McComb, J., Caldera, Y., & Randolph, P. (2003). Mindfulness meditation, anxiety reduction, and heart disease: a pilot study. Family & community health, 26(1), 25-33.
Lee, S. H., Ahn, S. C., Lee, Y. J., Choi, T. K., Yook, K. H., & Suh, S. Y. (2007). Effectiveness of a meditation-based stress management program as an adjunct to pharmacotherapy in patients with anxiety disorder. Journal of Psychosomatic Research, 62(2), 189-195.

However, one study by Heide and Borkovec describes the phenomena of relaxation induced anxiety (RIA):

While procedures such as progressive relaxation, biofeedback and meditation can often be effective in reducing subjective anxiety and physiological hyperactivity, recent evidence indicates that these same procedures apparently
  can initiate or exacerbate anxiety in certain individuals (Heide and Borkovec, 1983). 

They suggest that this may be because 

Somatic, affective and cognitive states arising during relaxation are perceived as threatening, perhaps due to the loss of control which they represent. Loss of control, in turn is avoided as either a perceived threat to coping and survival or perhaps more commonly as a threat to social acceptance (e.g. the fear of emerging inner conflicts and emotions, and the expression of which may be linked to anticipated social rejection). To guard against such loss of control, individuals may adopt strategies to cope with the
  environment and control anxiety; such strategies frequently maintain tension and may be antithetical to relaxation.

Based on this study, one would assume the effect of meditation is based on the individuals response to it, rather than the efficacy of the meditation techniques
Reference:
Heide, F. J., & Borkovec, T. D. (1984). Relaxation-induced anxiety: Mechanisms and theoretical implications. Behaviour research and therapy, 22(1), 1-12.

