Approximately 50% of late-stage HIV patients develop CXCR4-tropic (X4) virus in addition to CCR5-tropic (R5) virus. X4 emergence occurs with a sharp decline in CD4+ T cell counts and accelerated time to AIDS. Why this phenotypic switch to X4 occurs is not well understood. Previously, we used numerical simulations of a mathematical model to show that across much of parameter space a promising new class of antiretroviral treatments, CCR5 inhibitors, can accelerate X4 emergence and immunodeficiency. Here, we show that mathematical model to be a minimal activation-based HIV model that produces a spontaneous switch to X4 virus at a clinically-representative time point, while also matching in vivo data showing X4 and R5 coexisting and competing to infect memory CD4+ T cells. Our analysis shows that X4 avoids competitive exclusion from an initially fitter R5 virus due to X4v unique ability to productively infect nave CD4+ T cells. We further justify the generalized conditions under which this minimal model holds, implying that a phenotypic switch can even occur when the fraction of activated nave CD4+ T cells increases at a slower rate than the fraction of activated memory CD4+ T cells. We find that it is the ratio of the fractions of activated nave and memory CD4+ T cells that must increase above a threshold to produce a switch. This occurs as the concentration of CD4+ T cells drops beneath a threshold. Thus, highly active antiretroviral therapy (HAART), which increases CD4+ T cell counts and decreases cellular activation levels, inhibits X4 viral growth. However, we show here that even in the simplest dual-strain framework, competition between R5 and X4 viruses often results in accelerated X4 emergence in response to CCR5 inhibition, further highlighting the potential danger of anti-CCR5 monotherapy in multi-strain HIV infection.