GA pilot reported an NMAC during takeoff from TIW airport requiring evasive action. The pilot stated misinterpretation of ATC's clearance contributed to the event.

Narrative

I inadvertently deviated from an ATC command which resulted in a serious safety hazard in the traffic pattern of a class delta airport. The following information of my communications with ATC is to the best of my memory.Initially I was cleared by the tower to takeoff on Runway 17; but was to wait until further instruction before making my planned west departure. Tower then made a call to me and asked if I had the furthest downwind traffic in-sight (for a right traffic 17 pattern) to which I responded that I did. I noticed that at this point there were two aircraft on the downwind; one being close (would pass my wing within the minute) and the other being a great deal of distance away (2-3 minutes out). The next command that ATC gave me (to the best of my understanding) was to 'continue upwind until past the downwind traffic; and then make my west departure'. Unfortunately; I made a less-than-ideal radio call back to ATC restating their command in my own words. ATC then responded with 'make a west departure south of the traffic'. I repeated this command back to ATC and then attempted to correctly interpret the direction that was asked of me. I made a huge mental error and misjudged my directional awareness. I interpreted the ATC call reversed; which meant that I was to turn now; in-between the two aircraft. I initially hesitated to act on this because it seemed like a safety concern. I then considered thoughts that contributed to me incorrectly turning west in between the two aircraft on downwind; 'Why would ATC correct my first call if this isn't what they want me to do?' and 'What if there is something that ATC is seeing that I'm not; and if I don't turn now and continue upwind it would result in an ATC violation'. I then turned west; crosswind; and kept an eye on the traffic that was continuing downwind. I noticed that they began a climb to create separation between us; and I also began a small descent. In the AIM; it defines a near midair collision is within 500 feet. Due to my descent and their climb; and being in a high-wing aircraft; I could not visually confirm this distance (heights above were roughly estimated based off what I thought it might be); but I do know that we were uncomfortably close. I was confused at this point to what had occurred and a rush of adrenaline hit me. I thought again about my directional awareness and realized that I had made a massive error; and my senses were reversed. I had deviated from what ATC had asked of me; and jeopardized the safety of others in the vicinity. A huge pit developed in my stomach and I determined that owning my mistake was the best thing I could do. I made a massive mistake; and there were lessons to be learned. I hope that this report contributes to helping other pilots avoiding the mistake I did.Contributors to the ATC deviation and lessons learned - Fear - I let my fear of deviating from an ATC command trump my prioritization of safety. Even if ATC asked me to turn in between the two aircraft on downwind; I know that my duty as Pilot In Command (PIC) is to prioritize safety and I have the authority to do so in accordance with [the] CFRs. In the future I will continually strive to be assertive in ensuring safety. In this scenario if I applied this; the deviation would have been avoided.Lack of Situational Awareness - My failure to prioritize awareness contributed to this ATC deviation. If I would have been more alert to predicting ATC's command; and had better directional wits before taking off; I could have avoided this scenario. Simply briefing myself on the current traffic pattern called by ATC; checking the ADS-B flow; and directional awareness could have prevented this situation from happening.Lack of Confidence with ATC Communications - I assess that the confusion I caused on the tower frequency could have been avoided by practiced communications and a better understanding of the pilot controller glossary.Lack of Proficiency - In the last 8 months; I had less than 3 hours of flight time (all of which was in the last week and conducted with CFIs). Although I don't necessarily think that flying solo PIC was wrong at this point; this decreased my workload management capabilities and was a factor when combined with the other contributors.I have taken immediate action on these takeaways; and plan to continue implementing them. This event demonstrated some areas of much-needed improvement and it's not to be taken lightly.