Preventing itemize environment to insert initial vertical space

Lists like itemize act differently if they are used within a minipage environment. Specifically, they don't insert that vertical space before. So, you could use a minipage environment inside the table cell for the itemize list. There's a trick which is more handy - define this command:

\makeatletter
\newcommand*{\compress}{\@minipagetrue}
\makeatother

Now just use \compress before \begin{itemize}. You could even use it within the column definition, if you also load the array package:

\usepackage{array}
...
\begin{tabularx}{\textwidth}{>{\ttfamily}ll>{\compress}X}

Output of your example using this command:

The vertical space before itemize is gone. If you would like to compress the lists even more, have a look at

• the paralist package, which offers a compactitem environment for that purpose, or

• the enumitem package which allows easy customization of list environments, for example \begin{itemize}[itemsep=0pt], it even provides global configuration commands for lists.

But even with \begin{itemize}[itemsep=0pt,topsep=0pt] I would additionally use \compress.

Also consider something like this:

\usepackage{enumitem}
....
\begin{itemize}[nosep, leftmargin=5mm]
    \item Satisfy individual's needs for affiliation
    \item Develop individual's sense of identity
    \item Reduce individual's axiety and feelings of insecurity and powerlessness
\end{itemize}

The nosep kills all vertical spacing, leftmargin halves the horizontal space between the table left border and the bullets